# Tagged Questions

**12**

votes

**3**answers

1k views

### Are there 'analytic' $p$-adic modular forms.

The most elementary way to define $p$-adic modular forms is via limits of classical modular forms.
More precisely $f \in \mathbb{Z}_p[[q]]$ is called a $p$-adic modular form
if there are modular forms ...

**15**

votes

**3**answers

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### Non-vanishing of p-adic L-functions

In Non-vanishing of L-series of modular forms (easy case?) it was answered that for a cuspidal newform $f$ of weight strictly greater than 2, then $L(f,1)$ is non-zero. (Here the $L$-series is ...

**8**

votes

**1**answer

594 views

### Fields of definition for p-adic overconvergent modular eigenforms

If we consider the action of the $U_p$ operator on overconvergent $p$-adic modular forms, then we can get some information about the field over which the eigenforms are defined by looking at the ...

**7**

votes

**1**answer

441 views

### how do you evaluate the p-adic modular form E_p-1 in the region |j|<1

background/motivation
let Ek denote the modular form of level one and weight k with q-expansion given by $E_k(q)=1- \frac{2k}{b_k}\sum_n \sigma_{k-1}(n)q^n$ where σi is the divisor sum and bk ...

**7**

votes

**2**answers

973 views

### Free subquotient of Galois representations coming from Hida theory

Let $\mathbf{T}$ be the reduced nearly ordinary Hecke algebra of level $N$ of Hida theory for $\operatorname{GL}_{2}$ over $\mathbb{Q}$ (or more generally over a totally real field $F$). Then ...

**15**

votes

**3**answers

1k views

### 2-adic Coefficients of Modular Hecke Eigenforms.

Suppose that N is prime, and consider the normalized cuspidal Hecke eigenforms of weight 2 and level Gamma_0(N).
For such an eigenform f, the coefficients generate ...