The only CAS's that have built-in support for modular and automorphic forms, as far as I know, are Sage and Magma [edit: I had forgotten PARI/GP -- see Aurel's comment below]. Both offer roughly comparable functionality. In Sage you can do something like this:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.1, Release Date: 2017-12-07                     │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: S = Newforms(Gamma1(7), 4, names='a'); S
[q - q^2 - 2*q^3 - 7*q^4 + 16*q^5 + O(q^6),
 q + a1*q^2 + (-7/2*a1 - 7)*q^3 + (2*a1 + 4)*q^4 + 7/2*a1*q^5 + O(q^6)]
sage: f = S[0]
sage: f[next_prime(1000)]
-8930
sage: L = S[0].lseries()
sage: L(0.5 + 4.0*I)
6.68198475901674 + 1.21937727142056*I

William Stein (original author of most of this code) has written a wonderful book "Modular Forms -- A Computational Approach", which describes all the theory and algorithms, with copious Sage code examples.

You ask:

"Among them, I have in mind Mathematica, Maple, Magma, and also the Python-interface Sage. [...] Sage has the appeal to be free and open source, however I wonder if it is at the same level of the others."

Where modular forms are concerned, it's certainly not the case that Magma has a clear lead over Sage -- some functionality is better implemented in one or the other, but there's not an obvious winner overall. Both have flourishing user communities, regular updates, etc.

On the other hand, Mathematica and Maple are both completely useless as tools for number theory; they're great at symbolic manipulation of algebraic expressions, but that's more or less all they do. (I work on modular forms, and I can count on my fingers the number of times I've found Maple or Mathematica useful, whereas I use Sage and/or Magma every couple of weeks at least.)

The only CAS's that have built-in support for modular and automorphic forms, as far as I know, are Sage and Magma. [Edit: I had forgotten Pari/GP, which will introduce substantial modular forms functionality as of version 2.10 which is currently in alpha testing; see Aurel's comment below]. Both Sage and Magma offer roughly comparable functionality. In Sage you can do something like this:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.1, Release Date: 2017-12-07                     │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: S = Newforms(Gamma1(7), 4, names='a'); S
[q - q^2 - 2*q^3 - 7*q^4 + 16*q^5 + O(q^6),
 q + a1*q^2 + (-7/2*a1 - 7)*q^3 + (2*a1 + 4)*q^4 + 7/2*a1*q^5 + O(q^6)]
sage: f = S[0]
sage: f[next_prime(1000)]
-8930
sage: L = S[0].lseries()
sage: L(0.5 + 4.0*I)
6.68198475901674 + 1.21937727142056*I

William Stein (original author of most of this code) has written a wonderful book "Modular Forms -- A Computational Approach", which describes all the theory and algorithms, with copious Sage code examples.

You ask:

"Among them, I have in mind Mathematica, Maple, Magma, and also the Python-interface Sage. [...] Sage has the appeal to be free and open source, however I wonder if it is at the same level of the others."

Where modular forms are concerned, it's certainly not the case that Magma has a clear lead over Sage -- some functionality is better implemented in one or the other, but there's not an obvious winner overall. Both have flourishing user communities, regular updates, etc.

On the other hand, Mathematica and Maple are both completely useless as tools for number theory; they're great at symbolic manipulation of algebraic expressions, but that's more or less all they do. (I work on modular forms, and I can count on my fingers the number of times I've found Maple or Mathematica useful, whereas I use Sage and/or Magma every couple of weeks at least.)

The only CAS's that have built-in support for modular and automorphic forms, as far as I know, are Sage and Magma. Both offer roughly comparable functionality. In Sage you can do something like this:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.1, Release Date: 2017-12-07                     │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: S = Newforms(Gamma1(7), 4, names='a'); S
[q - q^2 - 2*q^3 - 7*q^4 + 16*q^5 + O(q^6),
 q + a1*q^2 + (-7/2*a1 - 7)*q^3 + (2*a1 + 4)*q^4 + 7/2*a1*q^5 + O(q^6)]
sage: f = S[0]
sage: f[next_prime(1000)]
-8930
sage: L = S[0].lseries()
sage: L(0.5 + 4.0*I)
6.68198475901674 + 1.21937727142056*I

William Stein (original author of most of this code) has written a wonderful book "Modular Forms -- A Computational Approach", which describes all the theory and algorithms, with copious Sage code examples.

You ask:

"Among them, I have in mind Mathematica, Maple, Magma, and also the Python-interface Sage. [...] Sage has the appeal to be free and open source, however I wonder if it is at the same level of the others."

Where modular forms are concerned, it's certainly not the case that Magma has a clear lead over Sage -- some functionality is better implemented in one or the other, but there's not an obvious winner overall. Both have flourishing user communities, regular updates, etc.

On the other hand, Mathematica and Maple are both completely useless as tools for number theory; they're great at symbolic manipulation of algebraic expressions, but that's more or less all they do. (I work on modular forms, and I can count on my fingers the number of times I've found Maple or Mathematica useful, whereas I use Sage and/or Magma every couple of weeks at least.)

The only CAS's that have built-in support for modular and automorphic forms, as far as I know, are Sage and Magma [edit: I had forgotten PARI/GP -- see Aurel's comment below]. Both offer roughly comparable functionality. In Sage you can do something like this:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.1, Release Date: 2017-12-07                     │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: S = Newforms(Gamma1(7), 4, names='a'); S
[q - q^2 - 2*q^3 - 7*q^4 + 16*q^5 + O(q^6),
 q + a1*q^2 + (-7/2*a1 - 7)*q^3 + (2*a1 + 4)*q^4 + 7/2*a1*q^5 + O(q^6)]
sage: f = S[0]
sage: f[next_prime(1000)]
-8930
sage: L = S[0].lseries()
sage: L(0.5 + 4.0*I)
6.68198475901674 + 1.21937727142056*I

William Stein (original author of most of this code) has written a wonderful book "Modular Forms -- A Computational Approach", which describes all the theory and algorithms, with copious Sage code examples.

You ask:

"Among them, I have in mind Mathematica, Maple, Magma, and also the Python-interface Sage. [...] Sage has the appeal to be free and open source, however I wonder if it is at the same level of the others."

Where modular forms are concerned, it's certainly not the case that Magma has a clear lead over Sage -- some functionality is better implemented in one or the other, but there's not an obvious winner overall. Both have flourishing user communities, regular updates, etc.

On the other hand, Mathematica and Maple are both completely useless as tools for number theory; they're great at symbolic manipulation of algebraic expressions, but that's more or less all they do. (I work on modular forms, and I can count on my fingers the number of times I've found Maple or Mathematica useful, whereas I use Sage and/or Magma every couple of weeks at least.)