Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1170))\).
|
Total |
New |
Old |
| Modular forms
| 37824 |
8672 |
29152 |
| Cusp forms
| 34753 |
8672 |
26081 |
| Eisenstein series
| 3071 |
0 |
3071 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1170))\)
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 |
| 1170.2.a |
\(\chi_{1170}(1, \cdot)\) |
1170.2.a.a |
1 |
1 |
| 1170.2.a.b |
1 |
| 1170.2.a.c |
1 |
| 1170.2.a.d |
1 |
| 1170.2.a.e |
1 |
| 1170.2.a.f |
1 |
| 1170.2.a.g |
1 |
| 1170.2.a.h |
1 |
| 1170.2.a.i |
1 |
| 1170.2.a.j |
1 |
| 1170.2.a.k |
1 |
| 1170.2.a.l |
1 |
| 1170.2.a.m |
1 |
| 1170.2.a.n |
1 |
| 1170.2.a.o |
2 |
| 1170.2.a.p |
2 |
| 1170.2.a.q |
2 |
| 1170.2.b |
\(\chi_{1170}(181, \cdot)\) |
1170.2.b.a |
2 |
1 |
| 1170.2.b.b |
2 |
| 1170.2.b.c |
2 |
| 1170.2.b.d |
4 |
| 1170.2.b.e |
4 |
| 1170.2.b.f |
4 |
| 1170.2.b.g |
8 |
| 1170.2.e |
\(\chi_{1170}(469, \cdot)\) |
1170.2.e.a |
2 |
1 |
| 1170.2.e.b |
2 |
| 1170.2.e.c |
2 |
| 1170.2.e.d |
2 |
| 1170.2.e.e |
4 |
| 1170.2.e.f |
6 |
| 1170.2.e.g |
6 |
| 1170.2.e.h |
6 |
| 1170.2.f |
\(\chi_{1170}(649, \cdot)\) |
1170.2.f.a |
4 |
1 |
| 1170.2.f.b |
4 |
| 1170.2.f.c |
6 |
| 1170.2.f.d |
6 |
| 1170.2.f.e |
8 |
| 1170.2.f.f |
8 |
| 1170.2.i |
\(\chi_{1170}(451, \cdot)\) |
1170.2.i.a |
2 |
2 |
| 1170.2.i.b |
2 |
| 1170.2.i.c |
2 |
| 1170.2.i.d |
2 |
| 1170.2.i.e |
2 |
| 1170.2.i.f |
2 |
| 1170.2.i.g |
2 |
| 1170.2.i.h |
2 |
| 1170.2.i.i |
2 |
| 1170.2.i.j |
2 |
| 1170.2.i.k |
2 |
| 1170.2.i.l |
2 |
| 1170.2.i.m |
4 |
| 1170.2.i.n |
4 |
| 1170.2.i.o |
4 |
| 1170.2.i.p |
4 |
| 1170.2.i.q |
4 |
| 1170.2.j |
\(\chi_{1170}(391, \cdot)\) |
1170.2.j.a |
2 |
2 |
| 1170.2.j.b |
2 |
| 1170.2.j.c |
2 |
| 1170.2.j.d |
2 |
| 1170.2.j.e |
2 |
| 1170.2.j.f |
2 |
| 1170.2.j.g |
4 |
| 1170.2.j.h |
8 |
| 1170.2.j.i |
10 |
| 1170.2.j.j |
10 |
| 1170.2.j.k |
12 |
| 1170.2.j.l |
12 |
| 1170.2.j.m |
12 |
| 1170.2.j.n |
16 |
| 1170.2.k |
\(\chi_{1170}(601, \cdot)\) |
n/a |
112 |
2 |
| 1170.2.l |
\(\chi_{1170}(61, \cdot)\) |
n/a |
112 |
2 |
| 1170.2.m |
\(\chi_{1170}(73, \cdot)\) |
1170.2.m.a |
2 |
2 |
| 1170.2.m.b |
2 |
| 1170.2.m.c |
2 |
| 1170.2.m.d |
4 |
| 1170.2.m.e |
4 |
| 1170.2.m.f |
12 |
| 1170.2.m.g |
14 |
| 1170.2.m.h |
14 |
| 1170.2.m.i |
16 |
| 1170.2.o |
\(\chi_{1170}(53, \cdot)\) |
1170.2.o.a |
12 |
2 |
| 1170.2.o.b |
12 |
| 1170.2.o.c |
12 |
| 1170.2.o.d |
12 |
| 1170.2.q |
\(\chi_{1170}(359, \cdot)\) |
1170.2.q.a |
4 |
2 |
| 1170.2.q.b |
4 |
| 1170.2.q.c |
24 |
| 1170.2.q.d |
24 |
| 1170.2.s |
\(\chi_{1170}(161, \cdot)\) |
1170.2.s.a |
4 |
2 |
| 1170.2.s.b |
4 |
| 1170.2.s.c |
4 |
| 1170.2.s.d |
4 |
| 1170.2.s.e |
8 |
| 1170.2.s.f |
12 |
| 1170.2.s.g |
12 |
| 1170.2.v |
\(\chi_{1170}(233, \cdot)\) |
1170.2.v.a |
4 |
2 |
| 1170.2.v.b |
4 |
| 1170.2.v.c |
24 |
| 1170.2.v.d |
24 |
| 1170.2.w |
\(\chi_{1170}(307, \cdot)\) |
1170.2.w.a |
2 |
2 |
| 1170.2.w.b |
2 |
| 1170.2.w.c |
2 |
| 1170.2.w.d |
4 |
| 1170.2.w.e |
4 |
| 1170.2.w.f |
12 |
| 1170.2.w.g |
14 |
| 1170.2.w.h |
14 |
| 1170.2.w.i |
16 |
| 1170.2.y |
\(\chi_{1170}(529, \cdot)\) |
n/a |
168 |
2 |
| 1170.2.bb |
\(\chi_{1170}(511, \cdot)\) |
n/a |
112 |
2 |
| 1170.2.bd |
\(\chi_{1170}(439, \cdot)\) |
n/a |
168 |
2 |
| 1170.2.bg |
\(\chi_{1170}(259, \cdot)\) |
n/a |
168 |
2 |
| 1170.2.bj |
\(\chi_{1170}(199, \cdot)\) |
1170.2.bj.a |
8 |
2 |
| 1170.2.bj.b |
8 |
| 1170.2.bj.c |
12 |
| 1170.2.bj.d |
12 |
| 1170.2.bj.e |
16 |
| 1170.2.bj.f |
16 |
| 1170.2.bm |
\(\chi_{1170}(121, \cdot)\) |
n/a |
112 |
2 |
| 1170.2.bo |
\(\chi_{1170}(79, \cdot)\) |
n/a |
144 |
2 |
| 1170.2.bp |
\(\chi_{1170}(289, \cdot)\) |
1170.2.bp.a |
4 |
2 |
| 1170.2.bp.b |
4 |
| 1170.2.bp.c |
4 |
| 1170.2.bp.d |
4 |
| 1170.2.bp.e |
4 |
| 1170.2.bp.f |
4 |
| 1170.2.bp.g |
8 |
| 1170.2.bp.h |
12 |
| 1170.2.bp.i |
24 |
| 1170.2.bs |
\(\chi_{1170}(361, \cdot)\) |
1170.2.bs.a |
4 |
2 |
| 1170.2.bs.b |
4 |
| 1170.2.bs.c |
4 |
| 1170.2.bs.d |
4 |
| 1170.2.bs.e |
4 |
| 1170.2.bs.f |
8 |
| 1170.2.bs.g |
8 |
| 1170.2.bs.h |
8 |
| 1170.2.bt |
\(\chi_{1170}(571, \cdot)\) |
n/a |
112 |
2 |
| 1170.2.bv |
\(\chi_{1170}(139, \cdot)\) |
n/a |
168 |
2 |
| 1170.2.bz |
\(\chi_{1170}(49, \cdot)\) |
n/a |
168 |
2 |
| 1170.2.cb |
\(\chi_{1170}(67, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.cc |
\(\chi_{1170}(223, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.cf |
\(\chi_{1170}(37, \cdot)\) |
n/a |
140 |
4 |
| 1170.2.cg |
\(\chi_{1170}(697, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.cj |
\(\chi_{1170}(113, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.cl |
\(\chi_{1170}(17, \cdot)\) |
n/a |
112 |
4 |
| 1170.2.cm |
\(\chi_{1170}(23, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.cp |
\(\chi_{1170}(77, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.cr |
\(\chi_{1170}(239, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.cs |
\(\chi_{1170}(11, \cdot)\) |
n/a |
224 |
4 |
| 1170.2.cu |
\(\chi_{1170}(71, \cdot)\) |
1170.2.cu.a |
8 |
4 |
| 1170.2.cu.b |
8 |
| 1170.2.cu.c |
8 |
| 1170.2.cu.d |
8 |
| 1170.2.cu.e |
16 |
| 1170.2.cu.f |
16 |
| 1170.2.cx |
\(\chi_{1170}(41, \cdot)\) |
n/a |
224 |
4 |
| 1170.2.cz |
\(\chi_{1170}(509, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.da |
\(\chi_{1170}(59, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.dc |
\(\chi_{1170}(89, \cdot)\) |
n/a |
112 |
4 |
| 1170.2.df |
\(\chi_{1170}(281, \cdot)\) |
n/a |
224 |
4 |
| 1170.2.dg |
\(\chi_{1170}(443, \cdot)\) |
n/a |
288 |
4 |
| 1170.2.dj |
\(\chi_{1170}(653, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.dk |
\(\chi_{1170}(107, \cdot)\) |
n/a |
112 |
4 |
| 1170.2.dm |
\(\chi_{1170}(563, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.do |
\(\chi_{1170}(457, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.dr |
\(\chi_{1170}(187, \cdot)\) |
n/a |
336 |
4 |
| 1170.2.ds |
\(\chi_{1170}(163, \cdot)\) |
n/a |
140 |
4 |
| 1170.2.dv |
\(\chi_{1170}(7, \cdot)\) |
n/a |
336 |
4 |
"n/a" means that newforms for that character have not been added to the database yet
