Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(555))\).
|
Total |
New |
Old |
Modular forms
| 11520 |
7723 |
3797 |
Cusp forms
| 10369 |
7307 |
3062 |
Eisenstein series
| 1151 |
416 |
735 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)
We only show spaces with even 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 |
555.2.a |
\(\chi_{555}(1, \cdot)\) |
555.2.a.a |
1 |
1 |
555.2.a.b |
1 |
555.2.a.c |
2 |
555.2.a.d |
2 |
555.2.a.e |
2 |
555.2.a.f |
2 |
555.2.a.g |
2 |
555.2.a.h |
3 |
555.2.a.i |
3 |
555.2.a.j |
5 |
555.2.c |
\(\chi_{555}(334, \cdot)\) |
555.2.c.a |
2 |
1 |
555.2.c.b |
8 |
555.2.c.c |
26 |
555.2.e |
\(\chi_{555}(406, \cdot)\) |
555.2.e.a |
2 |
1 |
555.2.e.b |
10 |
555.2.e.c |
12 |
555.2.g |
\(\chi_{555}(184, \cdot)\) |
555.2.g.a |
40 |
1 |
555.2.i |
\(\chi_{555}(121, \cdot)\) |
555.2.i.a |
2 |
2 |
555.2.i.b |
4 |
555.2.i.c |
4 |
555.2.i.d |
10 |
555.2.i.e |
14 |
555.2.i.f |
14 |
555.2.j |
\(\chi_{555}(43, \cdot)\) |
555.2.j.a |
76 |
2 |
555.2.m |
\(\chi_{555}(179, \cdot)\) |
555.2.m.a |
16 |
2 |
555.2.m.b |
128 |
555.2.n |
\(\chi_{555}(332, \cdot)\) |
555.2.n.a |
32 |
2 |
555.2.n.b |
112 |
555.2.o |
\(\chi_{555}(38, \cdot)\) |
555.2.o.a |
144 |
2 |
555.2.s |
\(\chi_{555}(191, \cdot)\) |
555.2.s.a |
104 |
2 |
555.2.t |
\(\chi_{555}(253, \cdot)\) |
555.2.t.a |
76 |
2 |
555.2.x |
\(\chi_{555}(64, \cdot)\) |
555.2.x.a |
80 |
2 |
555.2.z |
\(\chi_{555}(196, \cdot)\) |
555.2.z.a |
20 |
2 |
555.2.z.b |
28 |
555.2.bb |
\(\chi_{555}(454, \cdot)\) |
555.2.bb.a |
72 |
2 |
555.2.bc |
\(\chi_{555}(16, \cdot)\) |
555.2.bc.a |
6 |
6 |
555.2.bc.b |
36 |
555.2.bc.c |
36 |
555.2.bc.d |
36 |
555.2.bc.e |
42 |
555.2.bd |
\(\chi_{555}(82, \cdot)\) |
555.2.bd.a |
152 |
4 |
555.2.bg |
\(\chi_{555}(236, \cdot)\) |
555.2.bg.a |
208 |
4 |
555.2.bh |
\(\chi_{555}(122, \cdot)\) |
555.2.bh.a |
288 |
4 |
555.2.bi |
\(\chi_{555}(47, \cdot)\) |
555.2.bi.a |
288 |
4 |
555.2.bm |
\(\chi_{555}(14, \cdot)\) |
555.2.bm.a |
288 |
4 |
555.2.bn |
\(\chi_{555}(193, \cdot)\) |
555.2.bn.a |
152 |
4 |
555.2.bp |
\(\chi_{555}(4, \cdot)\) |
555.2.bp.a |
240 |
6 |
555.2.bs |
\(\chi_{555}(34, \cdot)\) |
555.2.bs.a |
216 |
6 |
555.2.bt |
\(\chi_{555}(136, \cdot)\) |
555.2.bt.a |
72 |
6 |
555.2.bt.b |
84 |
555.2.bx |
\(\chi_{555}(22, \cdot)\) |
555.2.bx.a |
456 |
12 |
555.2.bz |
\(\chi_{555}(56, \cdot)\) |
555.2.bz.a |
600 |
12 |
555.2.ca |
\(\chi_{555}(59, \cdot)\) |
555.2.ca.a |
864 |
12 |
555.2.cc |
\(\chi_{555}(53, \cdot)\) |
555.2.cc.a |
864 |
12 |
555.2.cf |
\(\chi_{555}(62, \cdot)\) |
555.2.cf.a |
864 |
12 |
555.2.ch |
\(\chi_{555}(13, \cdot)\) |
555.2.ch.a |
456 |
12 |