Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1890))\).
|
Total |
New |
Old |
Modular forms
| 96192 |
21592 |
74600 |
Cusp forms
| 90433 |
21592 |
68841 |
Eisenstein series
| 5759 |
0 |
5759 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1890))\)
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 available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
1890.2.a |
\(\chi_{1890}(1, \cdot)\) |
1890.2.a.a |
1 |
1 |
1890.2.a.b |
1 |
1890.2.a.c |
1 |
1890.2.a.d |
1 |
1890.2.a.e |
1 |
1890.2.a.f |
1 |
1890.2.a.g |
1 |
1890.2.a.h |
1 |
1890.2.a.i |
1 |
1890.2.a.j |
1 |
1890.2.a.k |
1 |
1890.2.a.l |
1 |
1890.2.a.m |
1 |
1890.2.a.n |
1 |
1890.2.a.o |
1 |
1890.2.a.p |
1 |
1890.2.a.q |
1 |
1890.2.a.r |
1 |
1890.2.a.s |
1 |
1890.2.a.t |
1 |
1890.2.a.u |
1 |
1890.2.a.v |
1 |
1890.2.a.w |
1 |
1890.2.a.x |
1 |
1890.2.a.y |
2 |
1890.2.a.z |
2 |
1890.2.a.ba |
2 |
1890.2.a.bb |
2 |
1890.2.b |
\(\chi_{1890}(1511, \cdot)\) |
1890.2.b.a |
8 |
1 |
1890.2.b.b |
8 |
1890.2.b.c |
12 |
1890.2.b.d |
12 |
1890.2.d |
\(\chi_{1890}(1889, \cdot)\) |
1890.2.d.a |
8 |
1 |
1890.2.d.b |
8 |
1890.2.d.c |
8 |
1890.2.d.d |
8 |
1890.2.d.e |
16 |
1890.2.d.f |
16 |
1890.2.g |
\(\chi_{1890}(379, \cdot)\) |
1890.2.g.a |
2 |
1 |
1890.2.g.b |
2 |
1890.2.g.c |
2 |
1890.2.g.d |
2 |
1890.2.g.e |
2 |
1890.2.g.f |
2 |
1890.2.g.g |
2 |
1890.2.g.h |
2 |
1890.2.g.i |
2 |
1890.2.g.j |
2 |
1890.2.g.k |
2 |
1890.2.g.l |
2 |
1890.2.g.m |
4 |
1890.2.g.n |
4 |
1890.2.g.o |
4 |
1890.2.g.p |
4 |
1890.2.g.q |
4 |
1890.2.g.r |
4 |
1890.2.i |
\(\chi_{1890}(991, \cdot)\) |
1890.2.i.a |
2 |
2 |
1890.2.i.b |
2 |
1890.2.i.c |
2 |
1890.2.i.d |
2 |
1890.2.i.e |
4 |
1890.2.i.f |
12 |
1890.2.i.g |
12 |
1890.2.i.h |
12 |
1890.2.i.i |
16 |
1890.2.j |
\(\chi_{1890}(631, \cdot)\) |
1890.2.j.a |
2 |
2 |
1890.2.j.b |
2 |
1890.2.j.c |
2 |
1890.2.j.d |
2 |
1890.2.j.e |
2 |
1890.2.j.f |
4 |
1890.2.j.g |
4 |
1890.2.j.h |
4 |
1890.2.j.i |
6 |
1890.2.j.j |
6 |
1890.2.j.k |
6 |
1890.2.j.l |
8 |
1890.2.k |
\(\chi_{1890}(541, \cdot)\) |
1890.2.k.a |
2 |
2 |
1890.2.k.b |
2 |
1890.2.k.c |
2 |
1890.2.k.d |
2 |
1890.2.k.e |
2 |
1890.2.k.f |
2 |
1890.2.k.g |
2 |
1890.2.k.h |
2 |
1890.2.k.i |
2 |
1890.2.k.j |
2 |
1890.2.k.k |
2 |
1890.2.k.l |
2 |
1890.2.k.m |
2 |
1890.2.k.n |
2 |
1890.2.k.o |
2 |
1890.2.k.p |
2 |
1890.2.k.q |
2 |
1890.2.k.r |
2 |
1890.2.k.s |
2 |
1890.2.k.t |
2 |
1890.2.k.u |
2 |
1890.2.k.v |
2 |
1890.2.k.w |
2 |
1890.2.k.x |
2 |
1890.2.k.y |
2 |
1890.2.k.z |
2 |
1890.2.k.ba |
2 |
1890.2.k.bb |
2 |
1890.2.k.bc |
2 |
1890.2.k.bd |
2 |
1890.2.k.be |
2 |
1890.2.k.bf |
2 |
1890.2.k.bg |
4 |
1890.2.k.bh |
4 |
1890.2.k.bi |
4 |
1890.2.k.bj |
4 |
1890.2.k.bk |
4 |
1890.2.k.bl |
4 |
1890.2.l |
\(\chi_{1890}(361, \cdot)\) |
1890.2.l.a |
2 |
2 |
1890.2.l.b |
2 |
1890.2.l.c |
2 |
1890.2.l.d |
2 |
1890.2.l.e |
4 |
1890.2.l.f |
12 |
1890.2.l.g |
12 |
1890.2.l.h |
12 |
1890.2.l.i |
16 |
1890.2.m |
\(\chi_{1890}(323, \cdot)\) |
1890.2.m.a |
24 |
2 |
1890.2.m.b |
24 |
1890.2.m.c |
24 |
1890.2.m.d |
24 |
1890.2.p |
\(\chi_{1890}(433, \cdot)\) |
n/a |
128 |
2 |
1890.2.r |
\(\chi_{1890}(89, \cdot)\) |
1890.2.r.a |
48 |
2 |
1890.2.r.b |
48 |
1890.2.t |
\(\chi_{1890}(1151, \cdot)\) |
1890.2.t.a |
4 |
2 |
1890.2.t.b |
28 |
1890.2.t.c |
32 |
1890.2.u |
\(\chi_{1890}(109, \cdot)\) |
n/a |
128 |
2 |
1890.2.z |
\(\chi_{1890}(1009, \cdot)\) |
1890.2.z.a |
4 |
2 |
1890.2.z.b |
24 |
1890.2.z.c |
44 |
1890.2.ba |
\(\chi_{1890}(1369, \cdot)\) |
1890.2.ba.a |
96 |
2 |
1890.2.be |
\(\chi_{1890}(971, \cdot)\) |
1890.2.be.a |
4 |
2 |
1890.2.be.b |
4 |
1890.2.be.c |
8 |
1890.2.be.d |
8 |
1890.2.be.e |
8 |
1890.2.be.f |
8 |
1890.2.be.g |
12 |
1890.2.be.h |
12 |
1890.2.be.i |
12 |
1890.2.be.j |
12 |
1890.2.bf |
\(\chi_{1890}(629, \cdot)\) |
1890.2.bf.a |
8 |
2 |
1890.2.bf.b |
8 |
1890.2.bf.c |
8 |
1890.2.bf.d |
8 |
1890.2.bf.e |
32 |
1890.2.bf.f |
32 |
1890.2.bi |
\(\chi_{1890}(719, \cdot)\) |
1890.2.bi.a |
48 |
2 |
1890.2.bi.b |
48 |
1890.2.bk |
\(\chi_{1890}(341, \cdot)\) |
1890.2.bk.a |
4 |
2 |
1890.2.bk.b |
28 |
1890.2.bk.c |
32 |
1890.2.bl |
\(\chi_{1890}(251, \cdot)\) |
1890.2.bl.a |
32 |
2 |
1890.2.bl.b |
32 |
1890.2.bo |
\(\chi_{1890}(269, \cdot)\) |
n/a |
128 |
2 |
1890.2.bq |
\(\chi_{1890}(289, \cdot)\) |
1890.2.bq.a |
96 |
2 |
1890.2.bs |
\(\chi_{1890}(211, \cdot)\) |
n/a |
432 |
6 |
1890.2.bt |
\(\chi_{1890}(331, \cdot)\) |
n/a |
576 |
6 |
1890.2.bu |
\(\chi_{1890}(121, \cdot)\) |
n/a |
576 |
6 |
1890.2.bw |
\(\chi_{1890}(557, \cdot)\) |
n/a |
192 |
4 |
1890.2.by |
\(\chi_{1890}(703, \cdot)\) |
n/a |
256 |
4 |
1890.2.bz |
\(\chi_{1890}(73, \cdot)\) |
n/a |
192 |
4 |
1890.2.cc |
\(\chi_{1890}(307, \cdot)\) |
n/a |
192 |
4 |
1890.2.cd |
\(\chi_{1890}(197, \cdot)\) |
n/a |
144 |
4 |
1890.2.cg |
\(\chi_{1890}(233, \cdot)\) |
n/a |
192 |
4 |
1890.2.ch |
\(\chi_{1890}(53, \cdot)\) |
n/a |
256 |
4 |
1890.2.cj |
\(\chi_{1890}(397, \cdot)\) |
n/a |
192 |
4 |
1890.2.cm |
\(\chi_{1890}(479, \cdot)\) |
n/a |
864 |
6 |
1890.2.co |
\(\chi_{1890}(499, \cdot)\) |
n/a |
864 |
6 |
1890.2.cs |
\(\chi_{1890}(41, \cdot)\) |
n/a |
576 |
6 |
1890.2.cu |
\(\chi_{1890}(311, \cdot)\) |
n/a |
576 |
6 |
1890.2.cv |
\(\chi_{1890}(79, \cdot)\) |
n/a |
864 |
6 |
1890.2.cx |
\(\chi_{1890}(169, \cdot)\) |
n/a |
648 |
6 |
1890.2.cz |
\(\chi_{1890}(59, \cdot)\) |
n/a |
864 |
6 |
1890.2.db |
\(\chi_{1890}(209, \cdot)\) |
n/a |
864 |
6 |
1890.2.dd |
\(\chi_{1890}(101, \cdot)\) |
n/a |
576 |
6 |
1890.2.dh |
\(\chi_{1890}(23, \cdot)\) |
n/a |
1728 |
12 |
1890.2.di |
\(\chi_{1890}(13, \cdot)\) |
n/a |
1728 |
12 |
1890.2.dj |
\(\chi_{1890}(157, \cdot)\) |
n/a |
1728 |
12 |
1890.2.do |
\(\chi_{1890}(113, \cdot)\) |
n/a |
1296 |
12 |
1890.2.dp |
\(\chi_{1890}(317, \cdot)\) |
n/a |
1728 |
12 |
1890.2.dq |
\(\chi_{1890}(103, \cdot)\) |
n/a |
1728 |
12 |
"n/a" means that newforms for that character have not been added to the database yet