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Properties

Label 7616.2
Level 7616
Weight 2
Dimension 943932
Nonzero newspaces 136
Sturm bound 7077888

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Defining parameters

Level: \( N \) = \( 7616 = 2^{6} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 136 \)
Sturm bound: \(7077888\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7616))\).

Total New Old
Modular forms 1783296 950532 832764
Cusp forms 1755649 943932 811717
Eisenstein series 27647 6600 21047

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7616))\)

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
7616.2.a \(\chi_{7616}(1, \cdot)\) 7616.2.a.a 1 1
7616.2.a.b 1
7616.2.a.c 1
7616.2.a.d 1
7616.2.a.e 1
7616.2.a.f 1
7616.2.a.g 1
7616.2.a.h 1
7616.2.a.i 1
7616.2.a.j 1
7616.2.a.k 1
7616.2.a.l 1
7616.2.a.m 2
7616.2.a.n 2
7616.2.a.o 2
7616.2.a.p 2
7616.2.a.q 2
7616.2.a.r 2
7616.2.a.s 2
7616.2.a.t 2
7616.2.a.u 2
7616.2.a.v 2
7616.2.a.w 2
7616.2.a.x 2
7616.2.a.y 2
7616.2.a.z 2
7616.2.a.ba 3
7616.2.a.bb 3
7616.2.a.bc 3
7616.2.a.bd 3
7616.2.a.be 3
7616.2.a.bf 3
7616.2.a.bg 3
7616.2.a.bh 3
7616.2.a.bi 4
7616.2.a.bj 4
7616.2.a.bk 4
7616.2.a.bl 4
7616.2.a.bm 4
7616.2.a.bn 4
7616.2.a.bo 4
7616.2.a.bp 4
7616.2.a.bq 5
7616.2.a.br 5
7616.2.a.bs 5
7616.2.a.bt 5
7616.2.a.bu 6
7616.2.a.bv 6
7616.2.a.bw 6
7616.2.a.bx 6
7616.2.a.by 6
7616.2.a.bz 6
7616.2.a.ca 6
7616.2.a.cb 6
7616.2.a.cc 6
7616.2.a.cd 6
7616.2.a.ce 8
7616.2.a.cf 8
7616.2.b \(\chi_{7616}(3809, \cdot)\) n/a 192 1
7616.2.c \(\chi_{7616}(4929, \cdot)\) n/a 216 1
7616.2.h \(\chi_{7616}(7615, \cdot)\) n/a 284 1
7616.2.i \(\chi_{7616}(6495, \cdot)\) n/a 256 1
7616.2.j \(\chi_{7616}(2687, \cdot)\) n/a 256 1
7616.2.k \(\chi_{7616}(3807, \cdot)\) n/a 288 1
7616.2.p \(\chi_{7616}(1121, \cdot)\) n/a 216 1
7616.2.q \(\chi_{7616}(1089, \cdot)\) n/a 512 2
7616.2.s \(\chi_{7616}(4815, \cdot)\) n/a 568 2
7616.2.t \(\chi_{7616}(5937, \cdot)\) n/a 432 2
7616.2.w \(\chi_{7616}(225, \cdot)\) n/a 432 2
7616.2.x \(\chi_{7616}(3583, \cdot)\) n/a 568 2
7616.2.z \(\chi_{7616}(1903, \cdot)\) n/a 568 2
7616.2.bc \(\chi_{7616}(783, \cdot)\) n/a 512 2
7616.2.be \(\chi_{7616}(1905, \cdot)\) n/a 384 2
7616.2.bf \(\chi_{7616}(3025, \cdot)\) n/a 432 2
7616.2.bi \(\chi_{7616}(897, \cdot)\) n/a 432 2
7616.2.bj \(\chi_{7616}(2911, \cdot)\) n/a 576 2
7616.2.bm \(\chi_{7616}(2129, \cdot)\) n/a 432 2
7616.2.bn \(\chi_{7616}(1007, \cdot)\) n/a 568 2
7616.2.bp \(\chi_{7616}(2209, \cdot)\) n/a 576 2
7616.2.bu \(\chi_{7616}(1599, \cdot)\) n/a 512 2
7616.2.bv \(\chi_{7616}(2719, \cdot)\) n/a 576 2
7616.2.bw \(\chi_{7616}(2175, \cdot)\) n/a 568 2
7616.2.bx \(\chi_{7616}(1055, \cdot)\) n/a 512 2
7616.2.cc \(\chi_{7616}(1633, \cdot)\) n/a 512 2
7616.2.cd \(\chi_{7616}(2753, \cdot)\) n/a 568 2
7616.2.cf \(\chi_{7616}(281, \cdot)\) None 0 4
7616.2.ch \(\chi_{7616}(1063, \cdot)\) None 0 4
7616.2.cj \(\chi_{7616}(1511, \cdot)\) None 0 4
7616.2.cl \(\chi_{7616}(841, \cdot)\) None 0 4
7616.2.cm \(\chi_{7616}(223, \cdot)\) n/a 1152 4
7616.2.co \(\chi_{7616}(1345, \cdot)\) n/a 864 4
7616.2.cq \(\chi_{7616}(727, \cdot)\) None 0 4
7616.2.ct \(\chi_{7616}(169, \cdot)\) None 0 4
7616.2.cv \(\chi_{7616}(953, \cdot)\) None 0 4
7616.2.cw \(\chi_{7616}(55, \cdot)\) None 0 4
7616.2.cy \(\chi_{7616}(559, \cdot)\) n/a 1136 4
7616.2.da \(\chi_{7616}(1681, \cdot)\) n/a 864 4
7616.2.dc \(\chi_{7616}(111, \cdot)\) n/a 1136 4
7616.2.de \(\chi_{7616}(1233, \cdot)\) n/a 864 4
7616.2.dh \(\chi_{7616}(1849, \cdot)\) None 0 4
7616.2.di \(\chi_{7616}(951, \cdot)\) None 0 4
7616.2.dk \(\chi_{7616}(1735, \cdot)\) None 0 4
7616.2.dn \(\chi_{7616}(1177, \cdot)\) None 0 4
7616.2.do \(\chi_{7616}(4031, \cdot)\) n/a 1136 4
7616.2.dq \(\chi_{7616}(5153, \cdot)\) n/a 864 4
7616.2.dt \(\chi_{7616}(2967, \cdot)\) None 0 4
7616.2.dv \(\chi_{7616}(729, \cdot)\) None 0 4
7616.2.dw \(\chi_{7616}(3415, \cdot)\) None 0 4
7616.2.dy \(\chi_{7616}(393, \cdot)\) None 0 4
7616.2.eb \(\chi_{7616}(591, \cdot)\) n/a 1136 4
7616.2.ec \(\chi_{7616}(625, \cdot)\) n/a 1136 4
7616.2.ee \(\chi_{7616}(1313, \cdot)\) n/a 1152 4
7616.2.eh \(\chi_{7616}(1279, \cdot)\) n/a 1136 4
7616.2.ei \(\chi_{7616}(2959, \cdot)\) n/a 1024 4
7616.2.el \(\chi_{7616}(271, \cdot)\) n/a 1136 4
7616.2.en \(\chi_{7616}(305, \cdot)\) n/a 1136 4
7616.2.eo \(\chi_{7616}(2993, \cdot)\) n/a 1024 4
7616.2.eq \(\chi_{7616}(1857, \cdot)\) n/a 1136 4
7616.2.et \(\chi_{7616}(1823, \cdot)\) n/a 1152 4
7616.2.ev \(\chi_{7616}(81, \cdot)\) n/a 1136 4
7616.2.ew \(\chi_{7616}(47, \cdot)\) n/a 1136 4
7616.2.ey \(\chi_{7616}(211, \cdot)\) n/a 6912 8
7616.2.fa \(\chi_{7616}(405, \cdot)\) n/a 9184 8
7616.2.fd \(\chi_{7616}(685, \cdot)\) n/a 9184 8
7616.2.ff \(\chi_{7616}(99, \cdot)\) n/a 6912 8
7616.2.fg \(\chi_{7616}(1133, \cdot)\) n/a 9184 8
7616.2.fi \(\chi_{7616}(1051, \cdot)\) n/a 6912 8
7616.2.fk \(\chi_{7616}(1469, \cdot)\) n/a 9184 8
7616.2.fm \(\chi_{7616}(267, \cdot)\) n/a 6912 8
7616.2.fp \(\chi_{7616}(911, \cdot)\) n/a 1728 8
7616.2.fr \(\chi_{7616}(657, \cdot)\) n/a 2272 8
7616.2.fs \(\chi_{7616}(365, \cdot)\) n/a 6912 8
7616.2.fw \(\chi_{7616}(1651, \cdot)\) n/a 9184 8
7616.2.fx \(\chi_{7616}(83, \cdot)\) n/a 9184 8
7616.2.fy \(\chi_{7616}(869, \cdot)\) n/a 6912 8
7616.2.ga \(\chi_{7616}(295, \cdot)\) None 0 8
7616.2.gc \(\chi_{7616}(601, \cdot)\) None 0 8
7616.2.gf \(\chi_{7616}(573, \cdot)\) n/a 9184 8
7616.2.gh \(\chi_{7616}(1357, \cdot)\) n/a 9184 8
7616.2.gj \(\chi_{7616}(1163, \cdot)\) n/a 6912 8
7616.2.gl \(\chi_{7616}(827, \cdot)\) n/a 6912 8
7616.2.gn \(\chi_{7616}(477, \cdot)\) n/a 6144 8
7616.2.gp \(\chi_{7616}(307, \cdot)\) n/a 8192 8
7616.2.gr \(\chi_{7616}(1303, \cdot)\) None 0 8
7616.2.gs \(\chi_{7616}(351, \cdot)\) n/a 1728 8
7616.2.gu \(\chi_{7616}(1373, \cdot)\) n/a 6912 8
7616.2.gx \(\chi_{7616}(421, \cdot)\) n/a 6912 8
7616.2.gz \(\chi_{7616}(575, \cdot)\) n/a 1728 8
7616.2.hb \(\chi_{7616}(71, \cdot)\) None 0 8
7616.2.hd \(\chi_{7616}(265, \cdot)\) None 0 8
7616.2.he \(\chi_{7616}(1217, \cdot)\) n/a 2272 8
7616.2.hh \(\chi_{7616}(251, \cdot)\) n/a 9184 8
7616.2.hi \(\chi_{7616}(1203, \cdot)\) n/a 9184 8
7616.2.hl \(\chi_{7616}(97, \cdot)\) n/a 2304 8
7616.2.hn \(\chi_{7616}(41, \cdot)\) None 0 8
7616.2.ho \(\chi_{7616}(645, \cdot)\) n/a 6912 8
7616.2.hq \(\chi_{7616}(475, \cdot)\) n/a 9184 8
7616.2.hs \(\chi_{7616}(855, \cdot)\) None 0 8
7616.2.hu \(\chi_{7616}(1945, \cdot)\) None 0 8
7616.2.hx \(\chi_{7616}(195, \cdot)\) n/a 9184 8
7616.2.hy \(\chi_{7616}(253, \cdot)\) n/a 6912 8
7616.2.hz \(\chi_{7616}(757, \cdot)\) n/a 6912 8
7616.2.id \(\chi_{7616}(1539, \cdot)\) n/a 9184 8
7616.2.if \(\chi_{7616}(687, \cdot)\) n/a 1728 8
7616.2.ih \(\chi_{7616}(209, \cdot)\) n/a 2272 8
7616.2.ij \(\chi_{7616}(181, \cdot)\) n/a 9184 8
7616.2.il \(\chi_{7616}(547, \cdot)\) n/a 6912 8
7616.2.im \(\chi_{7616}(125, \cdot)\) n/a 9184 8
7616.2.io \(\chi_{7616}(379, \cdot)\) n/a 6912 8
7616.2.iq \(\chi_{7616}(25, \cdot)\) None 0 8
7616.2.is \(\chi_{7616}(1895, \cdot)\) None 0 8
7616.2.iu \(\chi_{7616}(9, \cdot)\) None 0 8
7616.2.iw \(\chi_{7616}(1447, \cdot)\) None 0 8
7616.2.iz \(\chi_{7616}(961, \cdot)\) n/a 2272 8
7616.2.jb \(\chi_{7616}(927, \cdot)\) n/a 2304 8
7616.2.jd \(\chi_{7616}(999, \cdot)\) None 0 8
7616.2.je \(\chi_{7616}(137, \cdot)\) None 0 8
7616.2.jg \(\chi_{7616}(1257, \cdot)\) None 0 8
7616.2.jj \(\chi_{7616}(327, \cdot)\) None 0 8
7616.2.jl \(\chi_{7616}(977, \cdot)\) n/a 2272 8
7616.2.jn \(\chi_{7616}(943, \cdot)\) n/a 2272 8
7616.2.jp \(\chi_{7616}(529, \cdot)\) n/a 2272 8
7616.2.jr \(\chi_{7616}(495, \cdot)\) n/a 2272 8
7616.2.js \(\chi_{7616}(1033, \cdot)\) None 0 8
7616.2.jv \(\chi_{7616}(103, \cdot)\) None 0 8
7616.2.jx \(\chi_{7616}(1223, \cdot)\) None 0 8
7616.2.jy \(\chi_{7616}(361, \cdot)\) None 0 8
7616.2.kb \(\chi_{7616}(417, \cdot)\) n/a 2304 8
7616.2.kd \(\chi_{7616}(383, \cdot)\) n/a 2272 8
7616.2.ke \(\chi_{7616}(1929, \cdot)\) None 0 8
7616.2.kg \(\chi_{7616}(423, \cdot)\) None 0 8
7616.2.kj \(\chi_{7616}(87, \cdot)\) None 0 8
7616.2.kl \(\chi_{7616}(457, \cdot)\) None 0 8
7616.2.kn \(\chi_{7616}(683, \cdot)\) n/a 18368 16
7616.2.kp \(\chi_{7616}(5, \cdot)\) n/a 18368 16
7616.2.kq \(\chi_{7616}(347, \cdot)\) n/a 18368 16
7616.2.ks \(\chi_{7616}(1389, \cdot)\) n/a 18368 16
7616.2.ku \(\chi_{7616}(241, \cdot)\) n/a 4544 16
7616.2.kw \(\chi_{7616}(79, \cdot)\) n/a 4544 16
7616.2.kz \(\chi_{7616}(93, \cdot)\) n/a 18368 16
7616.2.la \(\chi_{7616}(19, \cdot)\) n/a 18368 16
7616.2.lb \(\chi_{7616}(59, \cdot)\) n/a 18368 16
7616.2.lf \(\chi_{7616}(53, \cdot)\) n/a 18368 16
7616.2.lg \(\chi_{7616}(201, \cdot)\) None 0 16
7616.2.li \(\chi_{7616}(471, \cdot)\) None 0 16
7616.2.ll \(\chi_{7616}(339, \cdot)\) n/a 18368 16
7616.2.ln \(\chi_{7616}(373, \cdot)\) n/a 18368 16
7616.2.lp \(\chi_{7616}(521, \cdot)\) None 0 16
7616.2.lr \(\chi_{7616}(481, \cdot)\) n/a 4608 16
7616.2.ls \(\chi_{7616}(115, \cdot)\) n/a 18368 16
7616.2.lv \(\chi_{7616}(523, \cdot)\) n/a 18368 16
7616.2.lw \(\chi_{7616}(129, \cdot)\) n/a 4544 16
7616.2.lz \(\chi_{7616}(873, \cdot)\) None 0 16
7616.2.mb \(\chi_{7616}(39, \cdot)\) None 0 16
7616.2.md \(\chi_{7616}(639, \cdot)\) n/a 4544 16
7616.2.mf \(\chi_{7616}(149, \cdot)\) n/a 18368 16
7616.2.mg \(\chi_{7616}(557, \cdot)\) n/a 18368 16
7616.2.mi \(\chi_{7616}(95, \cdot)\) n/a 4608 16
7616.2.ml \(\chi_{7616}(23, \cdot)\) None 0 16
7616.2.mm \(\chi_{7616}(171, \cdot)\) n/a 16384 16
7616.2.mo \(\chi_{7616}(205, \cdot)\) n/a 16384 16
7616.2.mq \(\chi_{7616}(275, \cdot)\) n/a 18368 16
7616.2.ms \(\chi_{7616}(1059, \cdot)\) n/a 18368 16
7616.2.mu \(\chi_{7616}(173, \cdot)\) n/a 18368 16
7616.2.mw \(\chi_{7616}(717, \cdot)\) n/a 18368 16
7616.2.my \(\chi_{7616}(73, \cdot)\) None 0 16
7616.2.na \(\chi_{7616}(487, \cdot)\) None 0 16
7616.2.nc \(\chi_{7616}(451, \cdot)\) n/a 18368 16
7616.2.ng \(\chi_{7616}(485, \cdot)\) n/a 18368 16
7616.2.nh \(\chi_{7616}(1845, \cdot)\) n/a 18368 16
7616.2.ni \(\chi_{7616}(1811, \cdot)\) n/a 18368 16
7616.2.nk \(\chi_{7616}(913, \cdot)\) n/a 4544 16
7616.2.nm \(\chi_{7616}(207, \cdot)\) n/a 4544 16
7616.2.np \(\chi_{7616}(499, \cdot)\) n/a 18368 16
7616.2.nr \(\chi_{7616}(45, \cdot)\) n/a 18368 16
7616.2.nt \(\chi_{7616}(107, \cdot)\) n/a 18368 16
7616.2.nv \(\chi_{7616}(381, \cdot)\) n/a 18368 16
7616.2.nw \(\chi_{7616}(11, \cdot)\) n/a 18368 16
7616.2.ny \(\chi_{7616}(845, \cdot)\) n/a 18368 16
7616.2.ob \(\chi_{7616}(549, \cdot)\) n/a 18368 16
7616.2.od \(\chi_{7616}(235, \cdot)\) n/a 18368 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7616))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7616)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(952))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1088))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1904))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3808))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7616))\)\(^{\oplus 1}\)