Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3997))\).
|
Total |
New |
Old |
Modular forms
| 3716 |
3136 |
580 |
Cusp forms
| 296 |
292 |
4 |
Eisenstein series
| 3420 |
2844 |
576 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3997))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
3997.1.b |
\(\chi_{3997}(2283, \cdot)\) |
None |
0 |
1 |
3997.1.d |
\(\chi_{3997}(1714, \cdot)\) |
None |
0 |
1 |
3997.1.j |
\(\chi_{3997}(681, \cdot)\) |
None |
0 |
2 |
3997.1.l |
\(\chi_{3997}(572, \cdot)\) |
None |
0 |
2 |
3997.1.m |
\(\chi_{3997}(1032, \cdot)\) |
None |
0 |
2 |
3997.1.n |
\(\chi_{3997}(461, \cdot)\) |
3997.1.n.a |
2 |
2 |
3997.1.n.b |
4 |
3997.1.n.c |
4 |
3997.1.r |
\(\chi_{3997}(2746, \cdot)\) |
None |
0 |
2 |
3997.1.s |
\(\chi_{3997}(1604, \cdot)\) |
None |
0 |
2 |
3997.1.t |
\(\chi_{3997}(1712, \cdot)\) |
None |
0 |
2 |
3997.1.u |
\(\chi_{3997}(2964, \cdot)\) |
None |
0 |
2 |
3997.1.w |
\(\chi_{3997}(2178, \cdot)\) |
None |
0 |
4 |
3997.1.x |
\(\chi_{3997}(167, \cdot)\) |
3997.1.x.a |
4 |
4 |
3997.1.be |
\(\chi_{3997}(240, \cdot)\) |
None |
0 |
8 |
3997.1.bf |
\(\chi_{3997}(468, \cdot)\) |
3997.1.bf.a |
8 |
8 |
3997.1.bg |
\(\chi_{3997}(255, \cdot)\) |
None |
0 |
8 |
3997.1.bh |
\(\chi_{3997}(481, \cdot)\) |
None |
0 |
8 |
3997.1.bi |
\(\chi_{3997}(184, \cdot)\) |
None |
0 |
8 |
3997.1.bj |
\(\chi_{3997}(71, \cdot)\) |
None |
0 |
8 |
3997.1.bk |
\(\chi_{3997}(669, \cdot)\) |
None |
0 |
8 |
3997.1.bo |
\(\chi_{3997}(500, \cdot)\) |
None |
0 |
8 |
3997.1.bp |
\(\chi_{3997}(55, \cdot)\) |
3997.1.bp.a |
18 |
18 |
3997.1.br |
\(\chi_{3997}(8, \cdot)\) |
None |
0 |
18 |
3997.1.bx |
\(\chi_{3997}(150, \cdot)\) |
None |
0 |
36 |
3997.1.by |
\(\chi_{3997}(221, \cdot)\) |
None |
0 |
36 |
3997.1.bz |
\(\chi_{3997}(85, \cdot)\) |
None |
0 |
36 |
3997.1.ca |
\(\chi_{3997}(58, \cdot)\) |
None |
0 |
36 |
3997.1.ce |
\(\chi_{3997}(258, \cdot)\) |
3997.1.ce.a |
36 |
36 |
3997.1.cf |
\(\chi_{3997}(82, \cdot)\) |
None |
0 |
36 |
3997.1.cg |
\(\chi_{3997}(31, \cdot)\) |
None |
0 |
36 |
3997.1.ci |
\(\chi_{3997}(2, \cdot)\) |
None |
0 |
36 |
3997.1.cj |
\(\chi_{3997}(6, \cdot)\) |
3997.1.cj.a |
72 |
72 |
3997.1.ck |
\(\chi_{3997}(15, \cdot)\) |
None |
0 |
72 |
3997.1.cq |
\(\chi_{3997}(5, \cdot)\) |
None |
0 |
144 |
3997.1.cu |
\(\chi_{3997}(39, \cdot)\) |
None |
0 |
144 |
3997.1.cv |
\(\chi_{3997}(113, \cdot)\) |
None |
0 |
144 |
3997.1.cw |
\(\chi_{3997}(86, \cdot)\) |
None |
0 |
144 |
3997.1.cx |
\(\chi_{3997}(38, \cdot)\) |
None |
0 |
144 |
3997.1.cy |
\(\chi_{3997}(52, \cdot)\) |
None |
0 |
144 |
3997.1.cz |
\(\chi_{3997}(13, \cdot)\) |
3997.1.cz.a |
144 |
144 |
3997.1.da |
\(\chi_{3997}(18, \cdot)\) |
None |
0 |
144 |