Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1920))\).
|
Total |
New |
Old |
Modular forms
| 100864 |
38304 |
62560 |
Cusp forms
| 95745 |
37728 |
58017 |
Eisenstein series
| 5119 |
576 |
4543 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1920))\)
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 |
1920.2.a |
\(\chi_{1920}(1, \cdot)\) |
1920.2.a.a |
1 |
1 |
1920.2.a.b |
1 |
1920.2.a.c |
1 |
1920.2.a.d |
1 |
1920.2.a.e |
1 |
1920.2.a.f |
1 |
1920.2.a.g |
1 |
1920.2.a.h |
1 |
1920.2.a.i |
1 |
1920.2.a.j |
1 |
1920.2.a.k |
1 |
1920.2.a.l |
1 |
1920.2.a.m |
1 |
1920.2.a.n |
1 |
1920.2.a.o |
1 |
1920.2.a.p |
1 |
1920.2.a.q |
1 |
1920.2.a.r |
1 |
1920.2.a.s |
1 |
1920.2.a.t |
1 |
1920.2.a.u |
1 |
1920.2.a.v |
1 |
1920.2.a.w |
1 |
1920.2.a.x |
1 |
1920.2.a.y |
2 |
1920.2.a.z |
2 |
1920.2.a.ba |
2 |
1920.2.a.bb |
2 |
1920.2.b |
\(\chi_{1920}(191, \cdot)\) |
1920.2.b.a |
8 |
1 |
1920.2.b.b |
8 |
1920.2.b.c |
8 |
1920.2.b.d |
8 |
1920.2.b.e |
8 |
1920.2.b.f |
8 |
1920.2.b.g |
8 |
1920.2.b.h |
8 |
1920.2.d |
\(\chi_{1920}(1729, \cdot)\) |
1920.2.d.a |
4 |
1 |
1920.2.d.b |
4 |
1920.2.d.c |
6 |
1920.2.d.d |
6 |
1920.2.d.e |
6 |
1920.2.d.f |
6 |
1920.2.d.g |
8 |
1920.2.d.h |
8 |
1920.2.f |
\(\chi_{1920}(769, \cdot)\) |
1920.2.f.a |
2 |
1 |
1920.2.f.b |
2 |
1920.2.f.c |
2 |
1920.2.f.d |
2 |
1920.2.f.e |
2 |
1920.2.f.f |
2 |
1920.2.f.g |
2 |
1920.2.f.h |
2 |
1920.2.f.i |
2 |
1920.2.f.j |
2 |
1920.2.f.k |
2 |
1920.2.f.l |
2 |
1920.2.f.m |
6 |
1920.2.f.n |
6 |
1920.2.f.o |
6 |
1920.2.f.p |
6 |
1920.2.h |
\(\chi_{1920}(1151, \cdot)\) |
1920.2.h.a |
4 |
1 |
1920.2.h.b |
4 |
1920.2.h.c |
4 |
1920.2.h.d |
4 |
1920.2.h.e |
4 |
1920.2.h.f |
4 |
1920.2.h.g |
4 |
1920.2.h.h |
4 |
1920.2.h.i |
4 |
1920.2.h.j |
4 |
1920.2.h.k |
4 |
1920.2.h.l |
4 |
1920.2.h.m |
4 |
1920.2.h.n |
4 |
1920.2.h.o |
4 |
1920.2.h.p |
4 |
1920.2.k |
\(\chi_{1920}(961, \cdot)\) |
1920.2.k.a |
2 |
1 |
1920.2.k.b |
2 |
1920.2.k.c |
2 |
1920.2.k.d |
2 |
1920.2.k.e |
2 |
1920.2.k.f |
2 |
1920.2.k.g |
2 |
1920.2.k.h |
2 |
1920.2.k.i |
4 |
1920.2.k.j |
4 |
1920.2.k.k |
4 |
1920.2.k.l |
4 |
1920.2.m |
\(\chi_{1920}(959, \cdot)\) |
1920.2.m.a |
4 |
1 |
1920.2.m.b |
4 |
1920.2.m.c |
4 |
1920.2.m.d |
4 |
1920.2.m.e |
4 |
1920.2.m.f |
4 |
1920.2.m.g |
4 |
1920.2.m.h |
4 |
1920.2.m.i |
4 |
1920.2.m.j |
4 |
1920.2.m.k |
4 |
1920.2.m.l |
4 |
1920.2.m.m |
4 |
1920.2.m.n |
4 |
1920.2.m.o |
4 |
1920.2.m.p |
4 |
1920.2.m.q |
4 |
1920.2.m.r |
4 |
1920.2.m.s |
4 |
1920.2.m.t |
4 |
1920.2.m.u |
4 |
1920.2.m.v |
4 |
1920.2.m.w |
8 |
1920.2.o |
\(\chi_{1920}(1919, \cdot)\) |
1920.2.o.a |
24 |
1 |
1920.2.o.b |
24 |
1920.2.o.c |
24 |
1920.2.o.d |
24 |
1920.2.s |
\(\chi_{1920}(481, \cdot)\) |
1920.2.s.a |
4 |
2 |
1920.2.s.b |
4 |
1920.2.s.c |
8 |
1920.2.s.d |
8 |
1920.2.s.e |
20 |
1920.2.s.f |
20 |
1920.2.t |
\(\chi_{1920}(479, \cdot)\) |
n/a |
176 |
2 |
1920.2.v |
\(\chi_{1920}(257, \cdot)\) |
n/a |
192 |
2 |
1920.2.w |
\(\chi_{1920}(127, \cdot)\) |
1920.2.w.a |
4 |
2 |
1920.2.w.b |
4 |
1920.2.w.c |
4 |
1920.2.w.d |
4 |
1920.2.w.e |
8 |
1920.2.w.f |
8 |
1920.2.w.g |
8 |
1920.2.w.h |
8 |
1920.2.w.i |
12 |
1920.2.w.j |
12 |
1920.2.w.k |
12 |
1920.2.w.l |
12 |
1920.2.y |
\(\chi_{1920}(223, \cdot)\) |
1920.2.y.a |
2 |
2 |
1920.2.y.b |
2 |
1920.2.y.c |
2 |
1920.2.y.d |
2 |
1920.2.y.e |
2 |
1920.2.y.f |
2 |
1920.2.y.g |
6 |
1920.2.y.h |
6 |
1920.2.y.i |
16 |
1920.2.y.j |
16 |
1920.2.y.k |
20 |
1920.2.y.l |
20 |
1920.2.bb |
\(\chi_{1920}(737, \cdot)\) |
n/a |
176 |
2 |
1920.2.bc |
\(\chi_{1920}(607, \cdot)\) |
1920.2.bc.a |
2 |
2 |
1920.2.bc.b |
2 |
1920.2.bc.c |
2 |
1920.2.bc.d |
2 |
1920.2.bc.e |
2 |
1920.2.bc.f |
2 |
1920.2.bc.g |
6 |
1920.2.bc.h |
6 |
1920.2.bc.i |
16 |
1920.2.bc.j |
16 |
1920.2.bc.k |
20 |
1920.2.bc.l |
20 |
1920.2.bf |
\(\chi_{1920}(353, \cdot)\) |
n/a |
176 |
2 |
1920.2.bh |
\(\chi_{1920}(703, \cdot)\) |
1920.2.bh.a |
4 |
2 |
1920.2.bh.b |
4 |
1920.2.bh.c |
4 |
1920.2.bh.d |
4 |
1920.2.bh.e |
4 |
1920.2.bh.f |
4 |
1920.2.bh.g |
4 |
1920.2.bh.h |
4 |
1920.2.bh.i |
8 |
1920.2.bh.j |
8 |
1920.2.bh.k |
12 |
1920.2.bh.l |
12 |
1920.2.bh.m |
12 |
1920.2.bh.n |
12 |
1920.2.bi |
\(\chi_{1920}(833, \cdot)\) |
n/a |
192 |
2 |
1920.2.bk |
\(\chi_{1920}(671, \cdot)\) |
n/a |
128 |
2 |
1920.2.bl |
\(\chi_{1920}(289, \cdot)\) |
1920.2.bl.a |
48 |
2 |
1920.2.bl.b |
48 |
1920.2.bo |
\(\chi_{1920}(367, \cdot)\) |
n/a |
192 |
4 |
1920.2.br |
\(\chi_{1920}(497, \cdot)\) |
n/a |
368 |
4 |
1920.2.bs |
\(\chi_{1920}(239, \cdot)\) |
n/a |
368 |
4 |
1920.2.bv |
\(\chi_{1920}(241, \cdot)\) |
n/a |
128 |
4 |
1920.2.bx |
\(\chi_{1920}(431, \cdot)\) |
n/a |
256 |
4 |
1920.2.by |
\(\chi_{1920}(49, \cdot)\) |
n/a |
192 |
4 |
1920.2.cb |
\(\chi_{1920}(17, \cdot)\) |
n/a |
368 |
4 |
1920.2.cc |
\(\chi_{1920}(847, \cdot)\) |
n/a |
192 |
4 |
1920.2.cf |
\(\chi_{1920}(233, \cdot)\) |
None |
0 |
8 |
1920.2.cg |
\(\chi_{1920}(103, \cdot)\) |
None |
0 |
8 |
1920.2.ci |
\(\chi_{1920}(121, \cdot)\) |
None |
0 |
8 |
1920.2.ck |
\(\chi_{1920}(169, \cdot)\) |
None |
0 |
8 |
1920.2.cn |
\(\chi_{1920}(71, \cdot)\) |
None |
0 |
8 |
1920.2.cp |
\(\chi_{1920}(119, \cdot)\) |
None |
0 |
8 |
1920.2.cr |
\(\chi_{1920}(137, \cdot)\) |
None |
0 |
8 |
1920.2.cs |
\(\chi_{1920}(7, \cdot)\) |
None |
0 |
8 |
1920.2.cw |
\(\chi_{1920}(173, \cdot)\) |
n/a |
6080 |
16 |
1920.2.cx |
\(\chi_{1920}(163, \cdot)\) |
n/a |
3072 |
16 |
1920.2.cy |
\(\chi_{1920}(11, \cdot)\) |
n/a |
4096 |
16 |
1920.2.cz |
\(\chi_{1920}(109, \cdot)\) |
n/a |
3072 |
16 |
1920.2.dc |
\(\chi_{1920}(61, \cdot)\) |
n/a |
2048 |
16 |
1920.2.dd |
\(\chi_{1920}(59, \cdot)\) |
n/a |
6080 |
16 |
1920.2.di |
\(\chi_{1920}(43, \cdot)\) |
n/a |
3072 |
16 |
1920.2.dj |
\(\chi_{1920}(53, \cdot)\) |
n/a |
6080 |
16 |
"n/a" means that newforms for that character have not been added to the database yet