↑

Properties

Label 8372.2
Level 8372
Weight 2
Dimension 1166868
Nonzero newspaces 120
Sturm bound 8515584

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 8372 = 2^{2} \cdot 7 \cdot 13 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(8515584\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8372))\).

Total New Old
Modular forms 2144736 1176116 968620
Cusp forms 2113057 1166868 946189
Eisenstein series 31679 9248 22431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8372))\)

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
8372.2.a \(\chi_{8372}(1, \cdot)\) 8372.2.a.a 1 1
8372.2.a.b 1
8372.2.a.c 1
8372.2.a.d 1
8372.2.a.e 1
8372.2.a.f 1
8372.2.a.g 1
8372.2.a.h 4
8372.2.a.i 8
8372.2.a.j 9
8372.2.a.k 15
8372.2.a.l 16
8372.2.a.m 16
8372.2.a.n 16
8372.2.a.o 20
8372.2.a.p 21
8372.2.c \(\chi_{8372}(183, \cdot)\) n/a 864 1
8372.2.d \(\chi_{8372}(4185, \cdot)\) n/a 224 1
8372.2.f \(\chi_{8372}(5979, \cdot)\) n/a 1008 1
8372.2.i \(\chi_{8372}(6761, \cdot)\) n/a 192 1
8372.2.k \(\chi_{8372}(6579, \cdot)\) n/a 1056 1
8372.2.l \(\chi_{8372}(5797, \cdot)\) n/a 152 1
8372.2.n \(\chi_{8372}(4003, \cdot)\) n/a 1232 1
8372.2.q \(\chi_{8372}(1381, \cdot)\) n/a 412 2
8372.2.r \(\chi_{8372}(4785, \cdot)\) n/a 352 2
8372.2.s \(\chi_{8372}(1933, \cdot)\) n/a 312 2
8372.2.t \(\chi_{8372}(737, \cdot)\) n/a 412 2
8372.2.v \(\chi_{8372}(967, \cdot)\) n/a 1848 2
8372.2.x \(\chi_{8372}(3037, \cdot)\) n/a 416 2
8372.2.y \(\chi_{8372}(3219, \cdot)\) n/a 2672 2
8372.2.ba \(\chi_{8372}(1149, \cdot)\) n/a 336 2
8372.2.bd \(\chi_{8372}(1517, \cdot)\) n/a 448 2
8372.2.be \(\chi_{8372}(2851, \cdot)\) n/a 2672 2
8372.2.bg \(\chi_{8372}(3449, \cdot)\) n/a 448 2
8372.2.bj \(\chi_{8372}(919, \cdot)\) n/a 2672 2
8372.2.bl \(\chi_{8372}(3221, \cdot)\) n/a 304 2
8372.2.bm \(\chi_{8372}(139, \cdot)\) n/a 2464 2
8372.2.bp \(\chi_{8372}(2623, \cdot)\) n/a 2464 2
8372.2.bt \(\chi_{8372}(5199, \cdot)\) n/a 2464 2
8372.2.bv \(\chi_{8372}(2209, \cdot)\) n/a 408 2
8372.2.bw \(\chi_{8372}(1795, \cdot)\) n/a 2112 2
8372.2.by \(\chi_{8372}(1979, \cdot)\) n/a 2464 2
8372.2.cb \(\chi_{8372}(277, \cdot)\) n/a 412 2
8372.2.ce \(\chi_{8372}(1427, \cdot)\) n/a 2464 2
8372.2.cg \(\chi_{8372}(1609, \cdot)\) n/a 448 2
8372.2.ch \(\chi_{8372}(2115, \cdot)\) n/a 2016 2
8372.2.cj \(\chi_{8372}(1977, \cdot)\) n/a 384 2
8372.2.cm \(\chi_{8372}(2391, \cdot)\) n/a 2672 2
8372.2.co \(\chi_{8372}(459, \cdot)\) n/a 2672 2
8372.2.cp \(\chi_{8372}(2161, \cdot)\) n/a 448 2
8372.2.cr \(\chi_{8372}(1563, \cdot)\) n/a 2672 2
8372.2.cu \(\chi_{8372}(2805, \cdot)\) n/a 448 2
8372.2.cw \(\chi_{8372}(5381, \cdot)\) n/a 448 2
8372.2.cx \(\chi_{8372}(4967, \cdot)\) n/a 2304 2
8372.2.cz \(\chi_{8372}(321, \cdot)\) n/a 448 2
8372.2.dc \(\chi_{8372}(3403, \cdot)\) n/a 2016 2
8372.2.de \(\chi_{8372}(3267, \cdot)\) n/a 2464 2
8372.2.dg \(\chi_{8372}(2669, \cdot)\) n/a 412 2
8372.2.dj \(\chi_{8372}(1335, \cdot)\) n/a 2464 2
8372.2.dk \(\chi_{8372}(729, \cdot)\) n/a 1440 10
8372.2.dl \(\chi_{8372}(1657, \cdot)\) n/a 824 4
8372.2.dn \(\chi_{8372}(1059, \cdot)\) n/a 4928 4
8372.2.dq \(\chi_{8372}(4231, \cdot)\) n/a 5344 4
8372.2.dr \(\chi_{8372}(505, \cdot)\) n/a 672 4
8372.2.du \(\chi_{8372}(1425, \cdot)\) n/a 896 4
8372.2.dv \(\chi_{8372}(643, \cdot)\) n/a 5344 4
8372.2.dy \(\chi_{8372}(551, \cdot)\) n/a 5344 4
8372.2.ea \(\chi_{8372}(137, \cdot)\) n/a 896 4
8372.2.eb \(\chi_{8372}(4279, \cdot)\) n/a 4928 4
8372.2.ee \(\chi_{8372}(461, \cdot)\) n/a 816 4
8372.2.ef \(\chi_{8372}(369, \cdot)\) n/a 816 4
8372.2.ei \(\chi_{8372}(323, \cdot)\) n/a 3696 4
8372.2.ej \(\chi_{8372}(1243, \cdot)\) n/a 4928 4
8372.2.el \(\chi_{8372}(4049, \cdot)\) n/a 824 4
8372.2.eo \(\chi_{8372}(1241, \cdot)\) n/a 896 4
8372.2.eq \(\chi_{8372}(1839, \cdot)\) n/a 5344 4
8372.2.et \(\chi_{8372}(363, \cdot)\) n/a 13360 10
8372.2.ev \(\chi_{8372}(1429, \cdot)\) n/a 1680 10
8372.2.ew \(\chi_{8372}(27, \cdot)\) n/a 11520 10
8372.2.ey \(\chi_{8372}(573, \cdot)\) n/a 1920 10
8372.2.fb \(\chi_{8372}(155, \cdot)\) n/a 10080 10
8372.2.fd \(\chi_{8372}(181, \cdot)\) n/a 2240 10
8372.2.fe \(\chi_{8372}(911, \cdot)\) n/a 8640 10
8372.2.fg \(\chi_{8372}(9, \cdot)\) n/a 4480 20
8372.2.fh \(\chi_{8372}(29, \cdot)\) n/a 3360 20
8372.2.fi \(\chi_{8372}(261, \cdot)\) n/a 3840 20
8372.2.fj \(\chi_{8372}(165, \cdot)\) n/a 4480 20
8372.2.fl \(\chi_{8372}(57, \cdot)\) n/a 3360 20
8372.2.fn \(\chi_{8372}(83, \cdot)\) n/a 26720 20
8372.2.fo \(\chi_{8372}(265, \cdot)\) n/a 4480 20
8372.2.fq \(\chi_{8372}(239, \cdot)\) n/a 20160 20
8372.2.fs \(\chi_{8372}(3, \cdot)\) n/a 26720 20
8372.2.fv \(\chi_{8372}(121, \cdot)\) n/a 4480 20
8372.2.fx \(\chi_{8372}(647, \cdot)\) n/a 26720 20
8372.2.fz \(\chi_{8372}(43, \cdot)\) n/a 20160 20
8372.2.gc \(\chi_{8372}(237, \cdot)\) n/a 4480 20
8372.2.ge \(\chi_{8372}(79, \cdot)\) n/a 23040 20
8372.2.gf \(\chi_{8372}(129, \cdot)\) n/a 4480 20
8372.2.gh \(\chi_{8372}(17, \cdot)\) n/a 4480 20
8372.2.gk \(\chi_{8372}(107, \cdot)\) n/a 26720 20
8372.2.gm \(\chi_{8372}(341, \cdot)\) n/a 4480 20
8372.2.gn \(\chi_{8372}(387, \cdot)\) n/a 26720 20
8372.2.gp \(\chi_{8372}(51, \cdot)\) n/a 26720 20
8372.2.gs \(\chi_{8372}(157, \cdot)\) n/a 3840 20
8372.2.gu \(\chi_{8372}(295, \cdot)\) n/a 20160 20
8372.2.gv \(\chi_{8372}(153, \cdot)\) n/a 4480 20
8372.2.gx \(\chi_{8372}(335, \cdot)\) n/a 26720 20
8372.2.ha \(\chi_{8372}(933, \cdot)\) n/a 4480 20
8372.2.hd \(\chi_{8372}(87, \cdot)\) n/a 26720 20
8372.2.hf \(\chi_{8372}(131, \cdot)\) n/a 23040 20
8372.2.hg \(\chi_{8372}(25, \cdot)\) n/a 4480 20
8372.2.hi \(\chi_{8372}(311, \cdot)\) n/a 26720 20
8372.2.hm \(\chi_{8372}(75, \cdot)\) n/a 26720 20
8372.2.hp \(\chi_{8372}(55, \cdot)\) n/a 26720 20
8372.2.hq \(\chi_{8372}(225, \cdot)\) n/a 3360 20
8372.2.hs \(\chi_{8372}(191, \cdot)\) n/a 26720 20
8372.2.hv \(\chi_{8372}(465, \cdot)\) n/a 4480 20
8372.2.hx \(\chi_{8372}(543, \cdot)\) n/a 26720 20
8372.2.hy \(\chi_{8372}(61, \cdot)\) n/a 4480 20
8372.2.ia \(\chi_{8372}(19, \cdot)\) n/a 53440 40
8372.2.ic \(\chi_{8372}(149, \cdot)\) n/a 8960 40
8372.2.if \(\chi_{8372}(409, \cdot)\) n/a 8960 40
8372.2.ih \(\chi_{8372}(151, \cdot)\) n/a 53440 40
8372.2.ii \(\chi_{8372}(71, \cdot)\) n/a 40320 40
8372.2.il \(\chi_{8372}(73, \cdot)\) n/a 8960 40
8372.2.im \(\chi_{8372}(41, \cdot)\) n/a 8960 40
8372.2.ip \(\chi_{8372}(123, \cdot)\) n/a 53440 40
8372.2.iq \(\chi_{8372}(37, \cdot)\) n/a 8960 40
8372.2.is \(\chi_{8372}(411, \cdot)\) n/a 53440 40
8372.2.iv \(\chi_{8372}(111, \cdot)\) n/a 53440 40
8372.2.iw \(\chi_{8372}(109, \cdot)\) n/a 8960 40
8372.2.iz \(\chi_{8372}(617, \cdot)\) n/a 6720 40
8372.2.ja \(\chi_{8372}(227, \cdot)\) n/a 53440 40
8372.2.jd \(\chi_{8372}(163, \cdot)\) n/a 53440 40
8372.2.jf \(\chi_{8372}(353, \cdot)\) n/a 8960 40

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8372))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8372)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(299))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(598))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2093))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4186))\)\(^{\oplus 2}\)