Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1700))\).
|
Total |
New |
Old |
Modular forms
| 2474 |
783 |
1691 |
Cusp forms
| 234 |
169 |
65 |
Eisenstein series
| 2240 |
614 |
1626 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1700))\)
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 |
1700.1.b |
\(\chi_{1700}(851, \cdot)\) |
None |
0 |
1 |
1700.1.d |
\(\chi_{1700}(1699, \cdot)\) |
1700.1.d.a |
2 |
1 |
1700.1.d.b |
2 |
1700.1.d.c |
2 |
1700.1.d.d |
4 |
1700.1.f |
\(\chi_{1700}(1599, \cdot)\) |
None |
0 |
1 |
1700.1.h |
\(\chi_{1700}(951, \cdot)\) |
1700.1.h.a |
1 |
1 |
1700.1.h.b |
1 |
1700.1.h.c |
1 |
1700.1.h.d |
1 |
1700.1.h.e |
1 |
1700.1.h.f |
2 |
1700.1.h.g |
2 |
1700.1.j |
\(\chi_{1700}(157, \cdot)\) |
None |
0 |
2 |
1700.1.k |
\(\chi_{1700}(1257, \cdot)\) |
None |
0 |
2 |
1700.1.n |
\(\chi_{1700}(599, \cdot)\) |
1700.1.n.a |
2 |
2 |
1700.1.n.b |
2 |
1700.1.p |
\(\chi_{1700}(251, \cdot)\) |
1700.1.p.a |
2 |
2 |
1700.1.q |
\(\chi_{1700}(1157, \cdot)\) |
None |
0 |
2 |
1700.1.t |
\(\chi_{1700}(293, \cdot)\) |
None |
0 |
2 |
1700.1.w |
\(\chi_{1700}(151, \cdot)\) |
1700.1.w.a |
4 |
4 |
1700.1.w.b |
4 |
1700.1.y |
\(\chi_{1700}(93, \cdot)\) |
None |
0 |
4 |
1700.1.z |
\(\chi_{1700}(393, \cdot)\) |
None |
0 |
4 |
1700.1.bb |
\(\chi_{1700}(399, \cdot)\) |
None |
0 |
4 |
1700.1.bd |
\(\chi_{1700}(271, \cdot)\) |
1700.1.bd.a |
4 |
4 |
1700.1.bd.b |
4 |
1700.1.bf |
\(\chi_{1700}(239, \cdot)\) |
None |
0 |
4 |
1700.1.bh |
\(\chi_{1700}(339, \cdot)\) |
None |
0 |
4 |
1700.1.bj |
\(\chi_{1700}(171, \cdot)\) |
None |
0 |
4 |
1700.1.bk |
\(\chi_{1700}(7, \cdot)\) |
1700.1.bk.a |
8 |
8 |
1700.1.bm |
\(\chi_{1700}(201, \cdot)\) |
None |
0 |
8 |
1700.1.bp |
\(\chi_{1700}(249, \cdot)\) |
None |
0 |
8 |
1700.1.br |
\(\chi_{1700}(107, \cdot)\) |
1700.1.br.a |
8 |
8 |
1700.1.bs |
\(\chi_{1700}(217, \cdot)\) |
None |
0 |
8 |
1700.1.bv |
\(\chi_{1700}(137, \cdot)\) |
None |
0 |
8 |
1700.1.bw |
\(\chi_{1700}(191, \cdot)\) |
1700.1.bw.a |
8 |
8 |
1700.1.bw.b |
8 |
1700.1.by |
\(\chi_{1700}(259, \cdot)\) |
None |
0 |
8 |
1700.1.cb |
\(\chi_{1700}(33, \cdot)\) |
None |
0 |
8 |
1700.1.cc |
\(\chi_{1700}(13, \cdot)\) |
None |
0 |
8 |
1700.1.cf |
\(\chi_{1700}(19, \cdot)\) |
1700.1.cf.a |
16 |
16 |
1700.1.cf.b |
16 |
1700.1.cg |
\(\chi_{1700}(117, \cdot)\) |
None |
0 |
16 |
1700.1.cj |
\(\chi_{1700}(53, \cdot)\) |
None |
0 |
16 |
1700.1.ck |
\(\chi_{1700}(111, \cdot)\) |
None |
0 |
16 |
1700.1.cm |
\(\chi_{1700}(23, \cdot)\) |
1700.1.cm.a |
32 |
32 |
1700.1.co |
\(\chi_{1700}(29, \cdot)\) |
None |
0 |
32 |
1700.1.cr |
\(\chi_{1700}(41, \cdot)\) |
None |
0 |
32 |
1700.1.ct |
\(\chi_{1700}(3, \cdot)\) |
1700.1.ct.a |
32 |
32 |