Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2368))\).
|
Total |
New |
Old |
Modular forms
| 177696 |
99122 |
78574 |
Cusp forms
| 172513 |
97582 |
74931 |
Eisenstein series
| 5183 |
1540 |
3643 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2368))\)
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 |
2368.2.a |
\(\chi_{2368}(1, \cdot)\) |
2368.2.a.a |
1 |
1 |
2368.2.a.b |
1 |
2368.2.a.c |
1 |
2368.2.a.d |
1 |
2368.2.a.e |
1 |
2368.2.a.f |
1 |
2368.2.a.g |
1 |
2368.2.a.h |
1 |
2368.2.a.i |
1 |
2368.2.a.j |
1 |
2368.2.a.k |
1 |
2368.2.a.l |
1 |
2368.2.a.m |
1 |
2368.2.a.n |
1 |
2368.2.a.o |
1 |
2368.2.a.p |
1 |
2368.2.a.q |
1 |
2368.2.a.r |
1 |
2368.2.a.s |
2 |
2368.2.a.t |
2 |
2368.2.a.u |
2 |
2368.2.a.v |
2 |
2368.2.a.w |
2 |
2368.2.a.x |
2 |
2368.2.a.y |
2 |
2368.2.a.z |
2 |
2368.2.a.ba |
2 |
2368.2.a.bb |
3 |
2368.2.a.bc |
3 |
2368.2.a.bd |
3 |
2368.2.a.be |
3 |
2368.2.a.bf |
4 |
2368.2.a.bg |
4 |
2368.2.a.bh |
4 |
2368.2.a.bi |
4 |
2368.2.a.bj |
8 |
2368.2.c |
\(\chi_{2368}(1185, \cdot)\) |
2368.2.c.a |
12 |
1 |
2368.2.c.b |
12 |
2368.2.c.c |
24 |
2368.2.c.d |
24 |
2368.2.e |
\(\chi_{2368}(2145, \cdot)\) |
2368.2.e.a |
8 |
1 |
2368.2.e.b |
20 |
2368.2.e.c |
48 |
2368.2.g |
\(\chi_{2368}(961, \cdot)\) |
2368.2.g.a |
2 |
1 |
2368.2.g.b |
2 |
2368.2.g.c |
2 |
2368.2.g.d |
2 |
2368.2.g.e |
2 |
2368.2.g.f |
2 |
2368.2.g.g |
2 |
2368.2.g.h |
4 |
2368.2.g.i |
4 |
2368.2.g.j |
4 |
2368.2.g.k |
6 |
2368.2.g.l |
6 |
2368.2.g.m |
8 |
2368.2.g.n |
8 |
2368.2.g.o |
10 |
2368.2.g.p |
10 |
2368.2.i |
\(\chi_{2368}(1025, \cdot)\) |
n/a |
148 |
2 |
2368.2.j |
\(\chi_{2368}(31, \cdot)\) |
n/a |
152 |
2 |
2368.2.m |
\(\chi_{2368}(623, \cdot)\) |
n/a |
148 |
2 |
2368.2.n |
\(\chi_{2368}(369, \cdot)\) |
n/a |
148 |
2 |
2368.2.o |
\(\chi_{2368}(593, \cdot)\) |
n/a |
144 |
2 |
2368.2.s |
\(\chi_{2368}(1807, \cdot)\) |
n/a |
148 |
2 |
2368.2.t |
\(\chi_{2368}(191, \cdot)\) |
n/a |
148 |
2 |
2368.2.w |
\(\chi_{2368}(1729, \cdot)\) |
n/a |
148 |
2 |
2368.2.y |
\(\chi_{2368}(545, \cdot)\) |
n/a |
152 |
2 |
2368.2.ba |
\(\chi_{2368}(417, \cdot)\) |
n/a |
152 |
2 |
2368.2.bc |
\(\chi_{2368}(297, \cdot)\) |
None |
0 |
4 |
2368.2.bf |
\(\chi_{2368}(487, \cdot)\) |
None |
0 |
4 |
2368.2.bh |
\(\chi_{2368}(327, \cdot)\) |
None |
0 |
4 |
2368.2.bj |
\(\chi_{2368}(73, \cdot)\) |
None |
0 |
4 |
2368.2.bk |
\(\chi_{2368}(641, \cdot)\) |
n/a |
444 |
6 |
2368.2.bm |
\(\chi_{2368}(319, \cdot)\) |
n/a |
296 |
4 |
2368.2.bn |
\(\chi_{2368}(399, \cdot)\) |
n/a |
296 |
4 |
2368.2.br |
\(\chi_{2368}(433, \cdot)\) |
n/a |
296 |
4 |
2368.2.bs |
\(\chi_{2368}(529, \cdot)\) |
n/a |
296 |
4 |
2368.2.bt |
\(\chi_{2368}(495, \cdot)\) |
n/a |
296 |
4 |
2368.2.bw |
\(\chi_{2368}(415, \cdot)\) |
n/a |
304 |
4 |
2368.2.by |
\(\chi_{2368}(43, \cdot)\) |
n/a |
2416 |
8 |
2368.2.ca |
\(\chi_{2368}(149, \cdot)\) |
n/a |
2304 |
8 |
2368.2.cc |
\(\chi_{2368}(221, \cdot)\) |
n/a |
2416 |
8 |
2368.2.cd |
\(\chi_{2368}(339, \cdot)\) |
n/a |
2416 |
8 |
2368.2.cg |
\(\chi_{2368}(65, \cdot)\) |
n/a |
444 |
6 |
2368.2.ci |
\(\chi_{2368}(33, \cdot)\) |
n/a |
456 |
6 |
2368.2.cl |
\(\chi_{2368}(225, \cdot)\) |
n/a |
456 |
6 |
2368.2.cm |
\(\chi_{2368}(233, \cdot)\) |
None |
0 |
8 |
2368.2.cp |
\(\chi_{2368}(615, \cdot)\) |
None |
0 |
8 |
2368.2.cr |
\(\chi_{2368}(23, \cdot)\) |
None |
0 |
8 |
2368.2.ct |
\(\chi_{2368}(121, \cdot)\) |
None |
0 |
8 |
2368.2.cv |
\(\chi_{2368}(383, \cdot)\) |
n/a |
888 |
12 |
2368.2.cw |
\(\chi_{2368}(337, \cdot)\) |
n/a |
888 |
12 |
2368.2.cy |
\(\chi_{2368}(15, \cdot)\) |
n/a |
888 |
12 |
2368.2.db |
\(\chi_{2368}(79, \cdot)\) |
n/a |
888 |
12 |
2368.2.dc |
\(\chi_{2368}(49, \cdot)\) |
n/a |
888 |
12 |
2368.2.df |
\(\chi_{2368}(351, \cdot)\) |
n/a |
912 |
12 |
2368.2.dh |
\(\chi_{2368}(251, \cdot)\) |
n/a |
4832 |
16 |
2368.2.dj |
\(\chi_{2368}(269, \cdot)\) |
n/a |
4832 |
16 |
2368.2.dl |
\(\chi_{2368}(85, \cdot)\) |
n/a |
4832 |
16 |
2368.2.dm |
\(\chi_{2368}(51, \cdot)\) |
n/a |
4832 |
16 |
2368.2.do |
\(\chi_{2368}(39, \cdot)\) |
None |
0 |
24 |
2368.2.dr |
\(\chi_{2368}(25, \cdot)\) |
None |
0 |
24 |
2368.2.dt |
\(\chi_{2368}(9, \cdot)\) |
None |
0 |
24 |
2368.2.du |
\(\chi_{2368}(55, \cdot)\) |
None |
0 |
24 |
2368.2.dw |
\(\chi_{2368}(53, \cdot)\) |
n/a |
14496 |
48 |
2368.2.ea |
\(\chi_{2368}(59, \cdot)\) |
n/a |
14496 |
48 |
2368.2.eb |
\(\chi_{2368}(19, \cdot)\) |
n/a |
14496 |
48 |
2368.2.ec |
\(\chi_{2368}(21, \cdot)\) |
n/a |
14496 |
48 |
"n/a" means that newforms for that character have not been added to the database yet