Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1344))\).
|
Total |
New |
Old |
Modular forms
| 50880 |
20092 |
30788 |
Cusp forms
| 47425 |
19652 |
27773 |
Eisenstein series
| 3455 |
440 |
3015 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1344))\)
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 |
1344.2.a |
\(\chi_{1344}(1, \cdot)\) |
1344.2.a.a |
1 |
1 |
1344.2.a.b |
1 |
1344.2.a.c |
1 |
1344.2.a.d |
1 |
1344.2.a.e |
1 |
1344.2.a.f |
1 |
1344.2.a.g |
1 |
1344.2.a.h |
1 |
1344.2.a.i |
1 |
1344.2.a.j |
1 |
1344.2.a.k |
1 |
1344.2.a.l |
1 |
1344.2.a.m |
1 |
1344.2.a.n |
1 |
1344.2.a.o |
1 |
1344.2.a.p |
1 |
1344.2.a.q |
1 |
1344.2.a.r |
1 |
1344.2.a.s |
1 |
1344.2.a.t |
1 |
1344.2.a.u |
2 |
1344.2.a.v |
2 |
1344.2.b |
\(\chi_{1344}(895, \cdot)\) |
1344.2.b.a |
2 |
1 |
1344.2.b.b |
2 |
1344.2.b.c |
2 |
1344.2.b.d |
2 |
1344.2.b.e |
4 |
1344.2.b.f |
4 |
1344.2.b.g |
8 |
1344.2.b.h |
8 |
1344.2.c |
\(\chi_{1344}(673, \cdot)\) |
1344.2.c.a |
2 |
1 |
1344.2.c.b |
2 |
1344.2.c.c |
2 |
1344.2.c.d |
2 |
1344.2.c.e |
4 |
1344.2.c.f |
4 |
1344.2.c.g |
4 |
1344.2.c.h |
4 |
1344.2.h |
\(\chi_{1344}(575, \cdot)\) |
1344.2.h.a |
4 |
1 |
1344.2.h.b |
4 |
1344.2.h.c |
4 |
1344.2.h.d |
4 |
1344.2.h.e |
4 |
1344.2.h.f |
8 |
1344.2.h.g |
8 |
1344.2.h.h |
12 |
1344.2.i |
\(\chi_{1344}(545, \cdot)\) |
1344.2.i.a |
4 |
1 |
1344.2.i.b |
4 |
1344.2.i.c |
8 |
1344.2.i.d |
8 |
1344.2.i.e |
8 |
1344.2.i.f |
16 |
1344.2.i.g |
16 |
1344.2.j |
\(\chi_{1344}(1247, \cdot)\) |
1344.2.j.a |
4 |
1 |
1344.2.j.b |
4 |
1344.2.j.c |
4 |
1344.2.j.d |
4 |
1344.2.j.e |
4 |
1344.2.j.f |
4 |
1344.2.j.g |
8 |
1344.2.j.h |
8 |
1344.2.j.i |
8 |
1344.2.k |
\(\chi_{1344}(1217, \cdot)\) |
1344.2.k.a |
2 |
1 |
1344.2.k.b |
2 |
1344.2.k.c |
4 |
1344.2.k.d |
4 |
1344.2.k.e |
8 |
1344.2.k.f |
8 |
1344.2.k.g |
8 |
1344.2.k.h |
8 |
1344.2.k.i |
8 |
1344.2.k.j |
8 |
1344.2.p |
\(\chi_{1344}(223, \cdot)\) |
1344.2.p.a |
4 |
1 |
1344.2.p.b |
4 |
1344.2.p.c |
12 |
1344.2.p.d |
12 |
1344.2.q |
\(\chi_{1344}(193, \cdot)\) |
1344.2.q.a |
2 |
2 |
1344.2.q.b |
2 |
1344.2.q.c |
2 |
1344.2.q.d |
2 |
1344.2.q.e |
2 |
1344.2.q.f |
2 |
1344.2.q.g |
2 |
1344.2.q.h |
2 |
1344.2.q.i |
2 |
1344.2.q.j |
2 |
1344.2.q.k |
2 |
1344.2.q.l |
2 |
1344.2.q.m |
2 |
1344.2.q.n |
2 |
1344.2.q.o |
2 |
1344.2.q.p |
2 |
1344.2.q.q |
2 |
1344.2.q.r |
2 |
1344.2.q.s |
2 |
1344.2.q.t |
2 |
1344.2.q.u |
2 |
1344.2.q.v |
2 |
1344.2.q.w |
4 |
1344.2.q.x |
4 |
1344.2.q.y |
6 |
1344.2.q.z |
6 |
1344.2.s |
\(\chi_{1344}(239, \cdot)\) |
1344.2.s.a |
4 |
2 |
1344.2.s.b |
4 |
1344.2.s.c |
40 |
1344.2.s.d |
48 |
1344.2.u |
\(\chi_{1344}(559, \cdot)\) |
1344.2.u.a |
64 |
2 |
1344.2.w |
\(\chi_{1344}(337, \cdot)\) |
1344.2.w.a |
20 |
2 |
1344.2.w.b |
28 |
1344.2.y |
\(\chi_{1344}(209, \cdot)\) |
n/a |
120 |
2 |
1344.2.bb |
\(\chi_{1344}(31, \cdot)\) |
1344.2.bb.a |
4 |
2 |
1344.2.bb.b |
4 |
1344.2.bb.c |
4 |
1344.2.bb.d |
4 |
1344.2.bb.e |
12 |
1344.2.bb.f |
12 |
1344.2.bb.g |
12 |
1344.2.bb.h |
12 |
1344.2.bc |
\(\chi_{1344}(257, \cdot)\) |
n/a |
120 |
2 |
1344.2.bd |
\(\chi_{1344}(95, \cdot)\) |
n/a |
128 |
2 |
1344.2.bi |
\(\chi_{1344}(353, \cdot)\) |
n/a |
128 |
2 |
1344.2.bj |
\(\chi_{1344}(191, \cdot)\) |
n/a |
120 |
2 |
1344.2.bk |
\(\chi_{1344}(289, \cdot)\) |
1344.2.bk.a |
4 |
2 |
1344.2.bk.b |
4 |
1344.2.bk.c |
4 |
1344.2.bk.d |
4 |
1344.2.bk.e |
4 |
1344.2.bk.f |
4 |
1344.2.bk.g |
4 |
1344.2.bk.h |
4 |
1344.2.bk.i |
8 |
1344.2.bk.j |
8 |
1344.2.bk.k |
8 |
1344.2.bk.l |
8 |
1344.2.bl |
\(\chi_{1344}(703, \cdot)\) |
1344.2.bl.a |
2 |
2 |
1344.2.bl.b |
2 |
1344.2.bl.c |
2 |
1344.2.bl.d |
2 |
1344.2.bl.e |
2 |
1344.2.bl.f |
2 |
1344.2.bl.g |
2 |
1344.2.bl.h |
2 |
1344.2.bl.i |
8 |
1344.2.bl.j |
8 |
1344.2.bl.k |
16 |
1344.2.bl.l |
16 |
1344.2.bo |
\(\chi_{1344}(41, \cdot)\) |
None |
0 |
4 |
1344.2.bq |
\(\chi_{1344}(169, \cdot)\) |
None |
0 |
4 |
1344.2.bs |
\(\chi_{1344}(71, \cdot)\) |
None |
0 |
4 |
1344.2.bu |
\(\chi_{1344}(55, \cdot)\) |
None |
0 |
4 |
1344.2.bw |
\(\chi_{1344}(17, \cdot)\) |
n/a |
240 |
4 |
1344.2.by |
\(\chi_{1344}(529, \cdot)\) |
n/a |
128 |
4 |
1344.2.ca |
\(\chi_{1344}(271, \cdot)\) |
n/a |
128 |
4 |
1344.2.cc |
\(\chi_{1344}(431, \cdot)\) |
n/a |
240 |
4 |
1344.2.cg |
\(\chi_{1344}(85, \cdot)\) |
n/a |
768 |
8 |
1344.2.ch |
\(\chi_{1344}(139, \cdot)\) |
n/a |
1024 |
8 |
1344.2.ci |
\(\chi_{1344}(155, \cdot)\) |
n/a |
1536 |
8 |
1344.2.cj |
\(\chi_{1344}(125, \cdot)\) |
n/a |
2016 |
8 |
1344.2.cn |
\(\chi_{1344}(103, \cdot)\) |
None |
0 |
8 |
1344.2.cp |
\(\chi_{1344}(23, \cdot)\) |
None |
0 |
8 |
1344.2.cr |
\(\chi_{1344}(25, \cdot)\) |
None |
0 |
8 |
1344.2.ct |
\(\chi_{1344}(89, \cdot)\) |
None |
0 |
8 |
1344.2.cw |
\(\chi_{1344}(5, \cdot)\) |
n/a |
4032 |
16 |
1344.2.cx |
\(\chi_{1344}(11, \cdot)\) |
n/a |
4032 |
16 |
1344.2.cy |
\(\chi_{1344}(19, \cdot)\) |
n/a |
2048 |
16 |
1344.2.cz |
\(\chi_{1344}(37, \cdot)\) |
n/a |
2048 |
16 |
"n/a" means that newforms for that character have not been added to the database yet