Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2352))\).
|
Total |
New |
Old |
Modular forms
| 153888 |
61375 |
92513 |
Cusp forms
| 147169 |
60503 |
86666 |
Eisenstein series
| 6719 |
872 |
5847 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2352))\)
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 |
2352.2.a |
\(\chi_{2352}(1, \cdot)\) |
2352.2.a.a |
1 |
1 |
2352.2.a.b |
1 |
2352.2.a.c |
1 |
2352.2.a.d |
1 |
2352.2.a.e |
1 |
2352.2.a.f |
1 |
2352.2.a.g |
1 |
2352.2.a.h |
1 |
2352.2.a.i |
1 |
2352.2.a.j |
1 |
2352.2.a.k |
1 |
2352.2.a.l |
1 |
2352.2.a.m |
1 |
2352.2.a.n |
1 |
2352.2.a.o |
1 |
2352.2.a.p |
1 |
2352.2.a.q |
1 |
2352.2.a.r |
1 |
2352.2.a.s |
1 |
2352.2.a.t |
1 |
2352.2.a.u |
1 |
2352.2.a.v |
1 |
2352.2.a.w |
1 |
2352.2.a.x |
1 |
2352.2.a.y |
1 |
2352.2.a.z |
2 |
2352.2.a.ba |
2 |
2352.2.a.bb |
2 |
2352.2.a.bc |
2 |
2352.2.a.bd |
2 |
2352.2.a.be |
2 |
2352.2.a.bf |
2 |
2352.2.a.bg |
2 |
2352.2.b |
\(\chi_{2352}(1567, \cdot)\) |
2352.2.b.a |
2 |
1 |
2352.2.b.b |
2 |
2352.2.b.c |
2 |
2352.2.b.d |
2 |
2352.2.b.e |
2 |
2352.2.b.f |
2 |
2352.2.b.g |
2 |
2352.2.b.h |
2 |
2352.2.b.i |
4 |
2352.2.b.j |
4 |
2352.2.b.k |
8 |
2352.2.b.l |
8 |
2352.2.c |
\(\chi_{2352}(1177, \cdot)\) |
None |
0 |
1 |
2352.2.h |
\(\chi_{2352}(2255, \cdot)\) |
2352.2.h.a |
2 |
1 |
2352.2.h.b |
2 |
2352.2.h.c |
2 |
2352.2.h.d |
2 |
2352.2.h.e |
2 |
2352.2.h.f |
4 |
2352.2.h.g |
4 |
2352.2.h.h |
4 |
2352.2.h.i |
4 |
2352.2.h.j |
4 |
2352.2.h.k |
4 |
2352.2.h.l |
8 |
2352.2.h.m |
8 |
2352.2.h.n |
8 |
2352.2.h.o |
8 |
2352.2.h.p |
16 |
2352.2.i |
\(\chi_{2352}(2057, \cdot)\) |
None |
0 |
1 |
2352.2.j |
\(\chi_{2352}(1079, \cdot)\) |
None |
0 |
1 |
2352.2.k |
\(\chi_{2352}(881, \cdot)\) |
2352.2.k.a |
2 |
1 |
2352.2.k.b |
2 |
2352.2.k.c |
2 |
2352.2.k.d |
2 |
2352.2.k.e |
4 |
2352.2.k.f |
8 |
2352.2.k.g |
8 |
2352.2.k.h |
8 |
2352.2.k.i |
16 |
2352.2.k.j |
24 |
2352.2.p |
\(\chi_{2352}(391, \cdot)\) |
None |
0 |
1 |
2352.2.q |
\(\chi_{2352}(961, \cdot)\) |
2352.2.q.a |
2 |
2 |
2352.2.q.b |
2 |
2352.2.q.c |
2 |
2352.2.q.d |
2 |
2352.2.q.e |
2 |
2352.2.q.f |
2 |
2352.2.q.g |
2 |
2352.2.q.h |
2 |
2352.2.q.i |
2 |
2352.2.q.j |
2 |
2352.2.q.k |
2 |
2352.2.q.l |
2 |
2352.2.q.m |
2 |
2352.2.q.n |
2 |
2352.2.q.o |
2 |
2352.2.q.p |
2 |
2352.2.q.q |
2 |
2352.2.q.r |
2 |
2352.2.q.s |
2 |
2352.2.q.t |
2 |
2352.2.q.u |
2 |
2352.2.q.v |
2 |
2352.2.q.w |
2 |
2352.2.q.x |
2 |
2352.2.q.y |
2 |
2352.2.q.z |
2 |
2352.2.q.ba |
4 |
2352.2.q.bb |
4 |
2352.2.q.bc |
4 |
2352.2.q.bd |
4 |
2352.2.q.be |
4 |
2352.2.q.bf |
4 |
2352.2.q.bg |
4 |
2352.2.s |
\(\chi_{2352}(491, \cdot)\) |
n/a |
636 |
2 |
2352.2.u |
\(\chi_{2352}(979, \cdot)\) |
n/a |
320 |
2 |
2352.2.w |
\(\chi_{2352}(589, \cdot)\) |
n/a |
328 |
2 |
2352.2.y |
\(\chi_{2352}(293, \cdot)\) |
n/a |
624 |
2 |
2352.2.bb |
\(\chi_{2352}(1207, \cdot)\) |
None |
0 |
2 |
2352.2.bc |
\(\chi_{2352}(1697, \cdot)\) |
n/a |
152 |
2 |
2352.2.bd |
\(\chi_{2352}(263, \cdot)\) |
None |
0 |
2 |
2352.2.bi |
\(\chi_{2352}(521, \cdot)\) |
None |
0 |
2 |
2352.2.bj |
\(\chi_{2352}(863, \cdot)\) |
n/a |
160 |
2 |
2352.2.bk |
\(\chi_{2352}(361, \cdot)\) |
None |
0 |
2 |
2352.2.bl |
\(\chi_{2352}(31, \cdot)\) |
2352.2.bl.a |
2 |
2 |
2352.2.bl.b |
2 |
2352.2.bl.c |
2 |
2352.2.bl.d |
2 |
2352.2.bl.e |
2 |
2352.2.bl.f |
2 |
2352.2.bl.g |
2 |
2352.2.bl.h |
2 |
2352.2.bl.i |
2 |
2352.2.bl.j |
2 |
2352.2.bl.k |
2 |
2352.2.bl.l |
2 |
2352.2.bl.m |
4 |
2352.2.bl.n |
4 |
2352.2.bl.o |
8 |
2352.2.bl.p |
8 |
2352.2.bl.q |
8 |
2352.2.bl.r |
8 |
2352.2.bl.s |
8 |
2352.2.bl.t |
8 |
2352.2.bo |
\(\chi_{2352}(337, \cdot)\) |
n/a |
336 |
6 |
2352.2.bp |
\(\chi_{2352}(509, \cdot)\) |
n/a |
1248 |
4 |
2352.2.br |
\(\chi_{2352}(373, \cdot)\) |
n/a |
640 |
4 |
2352.2.bt |
\(\chi_{2352}(19, \cdot)\) |
n/a |
640 |
4 |
2352.2.bv |
\(\chi_{2352}(275, \cdot)\) |
n/a |
1248 |
4 |
2352.2.bx |
\(\chi_{2352}(55, \cdot)\) |
None |
0 |
6 |
2352.2.cc |
\(\chi_{2352}(209, \cdot)\) |
n/a |
660 |
6 |
2352.2.cd |
\(\chi_{2352}(71, \cdot)\) |
None |
0 |
6 |
2352.2.ce |
\(\chi_{2352}(41, \cdot)\) |
None |
0 |
6 |
2352.2.cf |
\(\chi_{2352}(239, \cdot)\) |
n/a |
672 |
6 |
2352.2.ck |
\(\chi_{2352}(169, \cdot)\) |
None |
0 |
6 |
2352.2.cl |
\(\chi_{2352}(223, \cdot)\) |
n/a |
336 |
6 |
2352.2.cm |
\(\chi_{2352}(193, \cdot)\) |
n/a |
672 |
12 |
2352.2.cn |
\(\chi_{2352}(125, \cdot)\) |
n/a |
5328 |
12 |
2352.2.cp |
\(\chi_{2352}(85, \cdot)\) |
n/a |
2688 |
12 |
2352.2.cr |
\(\chi_{2352}(139, \cdot)\) |
n/a |
2688 |
12 |
2352.2.ct |
\(\chi_{2352}(155, \cdot)\) |
n/a |
5328 |
12 |
2352.2.cx |
\(\chi_{2352}(271, \cdot)\) |
n/a |
672 |
12 |
2352.2.cy |
\(\chi_{2352}(25, \cdot)\) |
None |
0 |
12 |
2352.2.cz |
\(\chi_{2352}(95, \cdot)\) |
n/a |
1344 |
12 |
2352.2.da |
\(\chi_{2352}(89, \cdot)\) |
None |
0 |
12 |
2352.2.df |
\(\chi_{2352}(23, \cdot)\) |
None |
0 |
12 |
2352.2.dg |
\(\chi_{2352}(17, \cdot)\) |
n/a |
1320 |
12 |
2352.2.dh |
\(\chi_{2352}(103, \cdot)\) |
None |
0 |
12 |
2352.2.dl |
\(\chi_{2352}(11, \cdot)\) |
n/a |
10656 |
24 |
2352.2.dn |
\(\chi_{2352}(115, \cdot)\) |
n/a |
5376 |
24 |
2352.2.dp |
\(\chi_{2352}(37, \cdot)\) |
n/a |
5376 |
24 |
2352.2.dr |
\(\chi_{2352}(5, \cdot)\) |
n/a |
10656 |
24 |
"n/a" means that newforms for that character have not been added to the database yet