Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1710))\).
|
Total |
New |
Old |
Modular forms
| 80064 |
18704 |
61360 |
Cusp forms
| 75457 |
18704 |
56753 |
Eisenstein series
| 4607 |
0 |
4607 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1710))\)
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 |
1710.2.a |
\(\chi_{1710}(1, \cdot)\) |
1710.2.a.a |
1 |
1 |
1710.2.a.b |
1 |
1710.2.a.c |
1 |
1710.2.a.d |
1 |
1710.2.a.e |
1 |
1710.2.a.f |
1 |
1710.2.a.g |
1 |
1710.2.a.h |
1 |
1710.2.a.i |
1 |
1710.2.a.j |
1 |
1710.2.a.k |
1 |
1710.2.a.l |
1 |
1710.2.a.m |
1 |
1710.2.a.n |
1 |
1710.2.a.o |
1 |
1710.2.a.p |
1 |
1710.2.a.q |
1 |
1710.2.a.r |
1 |
1710.2.a.s |
1 |
1710.2.a.t |
1 |
1710.2.a.u |
2 |
1710.2.a.v |
2 |
1710.2.a.w |
2 |
1710.2.a.x |
2 |
1710.2.a.y |
2 |
1710.2.c |
\(\chi_{1710}(1709, \cdot)\) |
1710.2.c.a |
4 |
1 |
1710.2.c.b |
4 |
1710.2.c.c |
8 |
1710.2.c.d |
24 |
1710.2.d |
\(\chi_{1710}(1369, \cdot)\) |
1710.2.d.a |
2 |
1 |
1710.2.d.b |
2 |
1710.2.d.c |
4 |
1710.2.d.d |
6 |
1710.2.d.e |
6 |
1710.2.d.f |
6 |
1710.2.d.g |
8 |
1710.2.d.h |
12 |
1710.2.f |
\(\chi_{1710}(341, \cdot)\) |
1710.2.f.a |
16 |
1 |
1710.2.f.b |
16 |
1710.2.i |
\(\chi_{1710}(121, \cdot)\) |
n/a |
160 |
2 |
1710.2.j |
\(\chi_{1710}(571, \cdot)\) |
n/a |
144 |
2 |
1710.2.k |
\(\chi_{1710}(391, \cdot)\) |
n/a |
160 |
2 |
1710.2.l |
\(\chi_{1710}(1261, \cdot)\) |
1710.2.l.a |
2 |
2 |
1710.2.l.b |
2 |
1710.2.l.c |
2 |
1710.2.l.d |
2 |
1710.2.l.e |
2 |
1710.2.l.f |
2 |
1710.2.l.g |
2 |
1710.2.l.h |
2 |
1710.2.l.i |
2 |
1710.2.l.j |
4 |
1710.2.l.k |
4 |
1710.2.l.l |
4 |
1710.2.l.m |
4 |
1710.2.l.n |
4 |
1710.2.l.o |
6 |
1710.2.l.p |
6 |
1710.2.l.q |
6 |
1710.2.l.r |
8 |
1710.2.l.s |
8 |
1710.2.n |
\(\chi_{1710}(647, \cdot)\) |
1710.2.n.a |
4 |
2 |
1710.2.n.b |
4 |
1710.2.n.c |
4 |
1710.2.n.d |
4 |
1710.2.n.e |
4 |
1710.2.n.f |
8 |
1710.2.n.g |
8 |
1710.2.n.h |
16 |
1710.2.n.i |
20 |
1710.2.p |
\(\chi_{1710}(37, \cdot)\) |
1710.2.p.a |
4 |
2 |
1710.2.p.b |
16 |
1710.2.p.c |
20 |
1710.2.p.d |
20 |
1710.2.p.e |
40 |
1710.2.q |
\(\chi_{1710}(179, \cdot)\) |
1710.2.q.a |
16 |
2 |
1710.2.q.b |
64 |
1710.2.t |
\(\chi_{1710}(919, \cdot)\) |
1710.2.t.a |
8 |
2 |
1710.2.t.b |
12 |
1710.2.t.c |
20 |
1710.2.t.d |
20 |
1710.2.t.e |
40 |
1710.2.x |
\(\chi_{1710}(1361, \cdot)\) |
n/a |
160 |
2 |
1710.2.ba |
\(\chi_{1710}(911, \cdot)\) |
n/a |
160 |
2 |
1710.2.bb |
\(\chi_{1710}(221, \cdot)\) |
n/a |
160 |
2 |
1710.2.bd |
\(\chi_{1710}(49, \cdot)\) |
n/a |
240 |
2 |
1710.2.bg |
\(\chi_{1710}(229, \cdot)\) |
n/a |
216 |
2 |
1710.2.bh |
\(\chi_{1710}(619, \cdot)\) |
n/a |
240 |
2 |
1710.2.bk |
\(\chi_{1710}(749, \cdot)\) |
n/a |
240 |
2 |
1710.2.bl |
\(\chi_{1710}(569, \cdot)\) |
n/a |
240 |
2 |
1710.2.bo |
\(\chi_{1710}(1019, \cdot)\) |
n/a |
240 |
2 |
1710.2.bq |
\(\chi_{1710}(521, \cdot)\) |
1710.2.bq.a |
32 |
2 |
1710.2.bq.b |
32 |
1710.2.bs |
\(\chi_{1710}(271, \cdot)\) |
n/a |
192 |
6 |
1710.2.bt |
\(\chi_{1710}(61, \cdot)\) |
n/a |
480 |
6 |
1710.2.bu |
\(\chi_{1710}(481, \cdot)\) |
n/a |
480 |
6 |
1710.2.bv |
\(\chi_{1710}(197, \cdot)\) |
n/a |
160 |
4 |
1710.2.by |
\(\chi_{1710}(493, \cdot)\) |
n/a |
480 |
4 |
1710.2.bz |
\(\chi_{1710}(103, \cdot)\) |
n/a |
480 |
4 |
1710.2.cc |
\(\chi_{1710}(373, \cdot)\) |
n/a |
480 |
4 |
1710.2.ce |
\(\chi_{1710}(77, \cdot)\) |
n/a |
432 |
4 |
1710.2.cf |
\(\chi_{1710}(83, \cdot)\) |
n/a |
480 |
4 |
1710.2.ci |
\(\chi_{1710}(353, \cdot)\) |
n/a |
480 |
4 |
1710.2.cj |
\(\chi_{1710}(217, \cdot)\) |
n/a |
200 |
4 |
1710.2.cl |
\(\chi_{1710}(139, \cdot)\) |
n/a |
720 |
6 |
1710.2.co |
\(\chi_{1710}(299, \cdot)\) |
n/a |
720 |
6 |
1710.2.cp |
\(\chi_{1710}(41, \cdot)\) |
n/a |
480 |
6 |
1710.2.ct |
\(\chi_{1710}(71, \cdot)\) |
n/a |
144 |
6 |
1710.2.cv |
\(\chi_{1710}(29, \cdot)\) |
n/a |
720 |
6 |
1710.2.cx |
\(\chi_{1710}(199, \cdot)\) |
n/a |
300 |
6 |
1710.2.da |
\(\chi_{1710}(89, \cdot)\) |
n/a |
240 |
6 |
1710.2.dc |
\(\chi_{1710}(499, \cdot)\) |
n/a |
720 |
6 |
1710.2.df |
\(\chi_{1710}(641, \cdot)\) |
n/a |
480 |
6 |
1710.2.dh |
\(\chi_{1710}(47, \cdot)\) |
n/a |
1440 |
12 |
1710.2.dk |
\(\chi_{1710}(13, \cdot)\) |
n/a |
1440 |
12 |
1710.2.dl |
\(\chi_{1710}(127, \cdot)\) |
n/a |
600 |
12 |
1710.2.dm |
\(\chi_{1710}(23, \cdot)\) |
n/a |
1440 |
12 |
1710.2.dn |
\(\chi_{1710}(17, \cdot)\) |
n/a |
480 |
12 |
1710.2.dq |
\(\chi_{1710}(193, \cdot)\) |
n/a |
1440 |
12 |
"n/a" means that newforms for that character have not been added to the database yet