Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(723))\).
|
Total |
New |
Old |
| Modular forms
| 519 |
277 |
242 |
| Cusp forms
| 39 |
39 |
0 |
| Eisenstein series
| 480 |
238 |
242 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(723))\)
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 |
| 723.1.b |
\(\chi_{723}(722, \cdot)\) |
723.1.b.a |
1 |
1 |
| 723.1.c |
\(\chi_{723}(242, \cdot)\) |
None |
0 |
1 |
| 723.1.g |
\(\chi_{723}(305, \cdot)\) |
723.1.g.a |
2 |
2 |
| 723.1.j |
\(\chi_{723}(497, \cdot)\) |
None |
0 |
2 |
| 723.1.k |
\(\chi_{723}(257, \cdot)\) |
None |
0 |
2 |
| 723.1.m |
\(\chi_{723}(8, \cdot)\) |
723.1.m.a |
4 |
4 |
| 723.1.n |
\(\chi_{723}(98, \cdot)\) |
723.1.n.a |
4 |
4 |
| 723.1.o |
\(\chi_{723}(143, \cdot)\) |
723.1.o.a |
4 |
4 |
| 723.1.q |
\(\chi_{723}(245, \cdot)\) |
None |
0 |
4 |
| 723.1.u |
\(\chi_{723}(76, \cdot)\) |
None |
0 |
8 |
| 723.1.w |
\(\chi_{723}(266, \cdot)\) |
723.1.w.a |
8 |
8 |
| 723.1.x |
\(\chi_{723}(2, \cdot)\) |
None |
0 |
8 |
| 723.1.ba |
\(\chi_{723}(122, \cdot)\) |
None |
0 |
8 |
| 723.1.bb |
\(\chi_{723}(119, \cdot)\) |
None |
0 |
8 |
| 723.1.bc |
\(\chi_{723}(5, \cdot)\) |
723.1.bc.a |
16 |
16 |
| 723.1.bf |
\(\chi_{723}(19, \cdot)\) |
None |
0 |
16 |
| 723.1.bg |
\(\chi_{723}(83, \cdot)\) |
None |
0 |
16 |
| 723.1.bi |
\(\chi_{723}(28, \cdot)\) |
None |
0 |
32 |
| 723.1.bl |
\(\chi_{723}(20, \cdot)\) |
None |
0 |
32 |
| 723.1.bm |
\(\chi_{723}(7, \cdot)\) |
None |
0 |
64 |
