# Properties

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

## 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 the 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

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