Timeline for Why is this vector space related to modular forms?
Current License: CC BY-SA 3.0
9 events
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| Jul 25, 2012 at 21:00 | history | edited | Jim Conant | CC BY-SA 3.0 |
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| Jul 20, 2012 at 13:43 | comment | added | Jim Conant | @Kevin: that's a good idea. | |
| Jul 20, 2012 at 13:42 | comment | added | Jim Conant | @Jeremy: could you elaborate? | |
| Jul 20, 2012 at 11:18 | comment | added | Jeremy Teitelbaum | This looks like a version of modular symbols to me. | |
| Jul 20, 2012 at 9:25 | comment | added | Kevin Buzzard | I'd be tempted to try and write down an isomorphism between your two spaces (and not think about modular forms at all). You've computed dimensions for $n$ small -- but why not compute some explicit bases, and try and spot an isomorphism. If you've already done this, then why not post the polynomials which span the six 1-dimensional spaces in both cases and see if anyone else can spot a link? Perhaps a basis for the first 2-dimensional space in each case might also help. I'm not saying this will definitely work, but it's perhaps worth a try. | |
| Jul 20, 2012 at 2:38 | comment | added | Jim Conant | I'm putting by bet on modular forms and not the A024160 sequence, but it's good to be aware of alternatives! | |
| Jul 20, 2012 at 2:22 | comment | added | Frank Thorne | @Barry: In the case of dimensions of spaces of cusp forms you have d(n + 12) = d(n) + 1, which is not true of the sequence you linked to. Indeed, this sequence is very simple: the space of modular forms for SL_2(\mathbb{Z}) is generated by Eisenstein series of weights 4 and 6, so the dimension of modular forms for weight n is the number of ways to write n=4a + 6b with a and b nonnegative integers. To get the dimension of the space of cusp forms, subtract 1. | |
| Jul 20, 2012 at 0:42 | comment | added | Barry Cipra | You may have already seen (and dismissed) this, but your sequence 0,0,0,0,1,0,1,1,1,1,2,1,2 shows up as part of oeis.org/A024160 | |
| Jul 20, 2012 at 0:17 | history | asked | Jim Conant | CC BY-SA 3.0 |