Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(737))\).
|
Total |
New |
Old |
Modular forms
| 692 |
616 |
76 |
Cusp forms
| 32 |
32 |
0 |
Eisenstein series
| 660 |
584 |
76 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(737))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
737.1.b |
\(\chi_{737}(133, \cdot)\) |
None |
0 |
1 |
737.1.c |
\(\chi_{737}(604, \cdot)\) |
None |
0 |
1 |
737.1.h |
\(\chi_{737}(298, \cdot)\) |
None |
0 |
2 |
737.1.i |
\(\chi_{737}(230, \cdot)\) |
737.1.i.a |
2 |
2 |
737.1.k |
\(\chi_{737}(68, \cdot)\) |
None |
0 |
4 |
737.1.l |
\(\chi_{737}(267, \cdot)\) |
None |
0 |
4 |
737.1.p |
\(\chi_{737}(76, \cdot)\) |
737.1.p.a |
10 |
10 |
737.1.q |
\(\chi_{737}(45, \cdot)\) |
None |
0 |
10 |
737.1.r |
\(\chi_{737}(29, \cdot)\) |
None |
0 |
8 |
737.1.s |
\(\chi_{737}(38, \cdot)\) |
None |
0 |
8 |
737.1.w |
\(\chi_{737}(10, \cdot)\) |
737.1.w.a |
20 |
20 |
737.1.x |
\(\chi_{737}(12, \cdot)\) |
None |
0 |
20 |
737.1.z |
\(\chi_{737}(3, \cdot)\) |
None |
0 |
40 |
737.1.ba |
\(\chi_{737}(24, \cdot)\) |
None |
0 |
40 |
737.1.be |
\(\chi_{737}(20, \cdot)\) |
None |
0 |
80 |
737.1.bf |
\(\chi_{737}(6, \cdot)\) |
None |
0 |
80 |