Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1407))\).
|
Total |
New |
Old |
Modular forms
| 1798 |
774 |
1024 |
Cusp forms
| 214 |
122 |
92 |
Eisenstein series
| 1584 |
652 |
932 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1407))\)
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 |
1407.1.b |
\(\chi_{1407}(736, \cdot)\) |
None |
0 |
1 |
1407.1.c |
\(\chi_{1407}(470, \cdot)\) |
None |
0 |
1 |
1407.1.f |
\(\chi_{1407}(202, \cdot)\) |
None |
0 |
1 |
1407.1.g |
\(\chi_{1407}(1406, \cdot)\) |
1407.1.g.a |
1 |
1 |
1407.1.g.b |
1 |
1407.1.g.c |
1 |
1407.1.g.d |
1 |
1407.1.g.e |
1 |
1407.1.g.f |
1 |
1407.1.g.g |
2 |
1407.1.g.h |
2 |
1407.1.g.i |
2 |
1407.1.g.j |
2 |
1407.1.o |
\(\chi_{1407}(431, \cdot)\) |
1407.1.o.a |
2 |
2 |
1407.1.p |
\(\chi_{1407}(172, \cdot)\) |
None |
0 |
2 |
1407.1.q |
\(\chi_{1407}(440, \cdot)\) |
None |
0 |
2 |
1407.1.r |
\(\chi_{1407}(1042, \cdot)\) |
None |
0 |
2 |
1407.1.u |
\(\chi_{1407}(164, \cdot)\) |
1407.1.u.a |
2 |
2 |
1407.1.v |
\(\chi_{1407}(565, \cdot)\) |
None |
0 |
2 |
1407.1.w |
\(\chi_{1407}(1006, \cdot)\) |
None |
0 |
2 |
1407.1.x |
\(\chi_{1407}(803, \cdot)\) |
None |
0 |
2 |
1407.1.z |
\(\chi_{1407}(29, \cdot)\) |
None |
0 |
2 |
1407.1.ba |
\(\chi_{1407}(1177, \cdot)\) |
None |
0 |
2 |
1407.1.bf |
\(\chi_{1407}(1138, \cdot)\) |
None |
0 |
2 |
1407.1.bg |
\(\chi_{1407}(872, \cdot)\) |
None |
0 |
2 |
1407.1.bh |
\(\chi_{1407}(305, \cdot)\) |
1407.1.bh.a |
2 |
2 |
1407.1.bi |
\(\chi_{1407}(298, \cdot)\) |
None |
0 |
2 |
1407.1.bm |
\(\chi_{1407}(38, \cdot)\) |
1407.1.bm.a |
2 |
2 |
1407.1.bn |
\(\chi_{1407}(439, \cdot)\) |
None |
0 |
2 |
1407.1.bq |
\(\chi_{1407}(125, \cdot)\) |
1407.1.bq.a |
10 |
10 |
1407.1.bq.b |
10 |
1407.1.br |
\(\chi_{1407}(76, \cdot)\) |
None |
0 |
10 |
1407.1.bu |
\(\chi_{1407}(92, \cdot)\) |
None |
0 |
10 |
1407.1.bv |
\(\chi_{1407}(43, \cdot)\) |
None |
0 |
10 |
1407.1.ca |
\(\chi_{1407}(19, \cdot)\) |
None |
0 |
20 |
1407.1.cb |
\(\chi_{1407}(101, \cdot)\) |
1407.1.cb.a |
20 |
20 |
1407.1.cf |
\(\chi_{1407}(79, \cdot)\) |
None |
0 |
20 |
1407.1.cg |
\(\chi_{1407}(116, \cdot)\) |
1407.1.cg.a |
20 |
20 |
1407.1.ch |
\(\chi_{1407}(107, \cdot)\) |
None |
0 |
20 |
1407.1.ci |
\(\chi_{1407}(58, \cdot)\) |
None |
0 |
20 |
1407.1.cn |
\(\chi_{1407}(85, \cdot)\) |
None |
0 |
20 |
1407.1.co |
\(\chi_{1407}(71, \cdot)\) |
None |
0 |
20 |
1407.1.cq |
\(\chi_{1407}(5, \cdot)\) |
None |
0 |
20 |
1407.1.cr |
\(\chi_{1407}(40, \cdot)\) |
None |
0 |
20 |
1407.1.cs |
\(\chi_{1407}(10, \cdot)\) |
None |
0 |
20 |
1407.1.ct |
\(\chi_{1407}(80, \cdot)\) |
1407.1.ct.a |
20 |
20 |
1407.1.cw |
\(\chi_{1407}(55, \cdot)\) |
None |
0 |
20 |
1407.1.cx |
\(\chi_{1407}(20, \cdot)\) |
None |
0 |
20 |
1407.1.cy |
\(\chi_{1407}(46, \cdot)\) |
None |
0 |
20 |
1407.1.cz |
\(\chi_{1407}(23, \cdot)\) |
1407.1.cz.a |
20 |
20 |