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Properties

Label 7752.2
Level 7752
Weight 2
Dimension 689080
Nonzero newspaces 90
Sturm bound 6635520

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Defining parameters

Level: \( N \) = \( 7752 = 2^{3} \cdot 3 \cdot 17 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 90 \)
Sturm bound: \(6635520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7752))\).

Total New Old
Modular forms 1672704 693160 979544
Cusp forms 1645057 689080 955977
Eisenstein series 27647 4080 23567

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7752))\)

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
7752.2.a \(\chi_{7752}(1, \cdot)\) 7752.2.a.a 1 1
7752.2.a.b 1
7752.2.a.c 1
7752.2.a.d 1
7752.2.a.e 1
7752.2.a.f 1
7752.2.a.g 1
7752.2.a.h 1
7752.2.a.i 1
7752.2.a.j 1
7752.2.a.k 1
7752.2.a.l 2
7752.2.a.m 2
7752.2.a.n 5
7752.2.a.o 6
7752.2.a.p 6
7752.2.a.q 6
7752.2.a.r 7
7752.2.a.s 7
7752.2.a.t 7
7752.2.a.u 8
7752.2.a.v 8
7752.2.a.w 8
7752.2.a.x 8
7752.2.a.y 9
7752.2.a.z 10
7752.2.a.ba 10
7752.2.a.bb 11
7752.2.a.bc 13
7752.2.d \(\chi_{7752}(5473, \cdot)\) n/a 160 1
7752.2.e \(\chi_{7752}(5813, \cdot)\) n/a 1432 1
7752.2.h \(\chi_{7752}(3571, \cdot)\) n/a 640 1
7752.2.i \(\chi_{7752}(647, \cdot)\) None 0 1
7752.2.j \(\chi_{7752}(4217, \cdot)\) n/a 320 1
7752.2.k \(\chi_{7752}(3877, \cdot)\) n/a 576 1
7752.2.n \(\chi_{7752}(2243, \cdot)\) n/a 1296 1
7752.2.o \(\chi_{7752}(5167, \cdot)\) None 0 1
7752.2.r \(\chi_{7752}(7447, \cdot)\) None 0 1
7752.2.s \(\chi_{7752}(4523, \cdot)\) n/a 1152 1
7752.2.v \(\chi_{7752}(1597, \cdot)\) n/a 648 1
7752.2.w \(\chi_{7752}(1937, \cdot)\) n/a 360 1
7752.2.bb \(\chi_{7752}(6119, \cdot)\) None 0 1
7752.2.bc \(\chi_{7752}(1291, \cdot)\) n/a 720 1
7752.2.bf \(\chi_{7752}(341, \cdot)\) n/a 1280 1
7752.2.bg \(\chi_{7752}(2857, \cdot)\) n/a 320 2
7752.2.bh \(\chi_{7752}(2393, \cdot)\) n/a 720 2
7752.2.bi \(\chi_{7752}(2699, \cdot)\) n/a 2592 2
7752.2.bj \(\chi_{7752}(5623, \cdot)\) None 0 2
7752.2.bk \(\chi_{7752}(2053, \cdot)\) n/a 1296 2
7752.2.bt \(\chi_{7752}(1747, \cdot)\) n/a 1440 2
7752.2.bu \(\chi_{7752}(5929, \cdot)\) n/a 320 2
7752.2.bv \(\chi_{7752}(6269, \cdot)\) n/a 2864 2
7752.2.bw \(\chi_{7752}(191, \cdot)\) None 0 2
7752.2.bz \(\chi_{7752}(4115, \cdot)\) n/a 2560 2
7752.2.ca \(\chi_{7752}(103, \cdot)\) None 0 2
7752.2.cd \(\chi_{7752}(2345, \cdot)\) n/a 720 2
7752.2.ce \(\chi_{7752}(1189, \cdot)\) n/a 1440 2
7752.2.cf \(\chi_{7752}(1699, \cdot)\) n/a 1440 2
7752.2.cg \(\chi_{7752}(1223, \cdot)\) None 0 2
7752.2.cj \(\chi_{7752}(749, \cdot)\) n/a 2560 2
7752.2.cm \(\chi_{7752}(2957, \cdot)\) n/a 2864 2
7752.2.cn \(\chi_{7752}(577, \cdot)\) n/a 360 2
7752.2.cq \(\chi_{7752}(239, \cdot)\) None 0 2
7752.2.cr \(\chi_{7752}(715, \cdot)\) n/a 1280 2
7752.2.cw \(\chi_{7752}(3469, \cdot)\) n/a 1280 2
7752.2.cx \(\chi_{7752}(1361, \cdot)\) n/a 640 2
7752.2.da \(\chi_{7752}(2311, \cdot)\) None 0 2
7752.2.db \(\chi_{7752}(1835, \cdot)\) n/a 2864 2
7752.2.dg \(\chi_{7752}(457, \cdot)\) n/a 656 4
7752.2.dh \(\chi_{7752}(1103, \cdot)\) None 0 4
7752.2.di \(\chi_{7752}(797, \cdot)\) n/a 5728 4
7752.2.dj \(\chi_{7752}(835, \cdot)\) n/a 2880 4
7752.2.dk \(\chi_{7752}(229, \cdot)\) n/a 2592 4
7752.2.dl \(\chi_{7752}(875, \cdot)\) n/a 5184 4
7752.2.dm \(\chi_{7752}(569, \cdot)\) n/a 1440 4
7752.2.dn \(\chi_{7752}(151, \cdot)\) None 0 4
7752.2.ds \(\chi_{7752}(1225, \cdot)\) n/a 960 6
7752.2.dt \(\chi_{7752}(1679, \cdot)\) None 0 4
7752.2.du \(\chi_{7752}(293, \cdot)\) n/a 5728 4
7752.2.dv \(\chi_{7752}(1033, \cdot)\) n/a 720 4
7752.2.dw \(\chi_{7752}(259, \cdot)\) n/a 2880 4
7752.2.ef \(\chi_{7752}(1645, \cdot)\) n/a 2880 4
7752.2.eg \(\chi_{7752}(2767, \cdot)\) None 0 4
7752.2.eh \(\chi_{7752}(2291, \cdot)\) n/a 5728 4
7752.2.ei \(\chi_{7752}(905, \cdot)\) n/a 1440 4
7752.2.el \(\chi_{7752}(37, \cdot)\) n/a 5760 8
7752.2.em \(\chi_{7752}(1217, \cdot)\) n/a 2592 8
7752.2.en \(\chi_{7752}(343, \cdot)\) None 0 8
7752.2.eo \(\chi_{7752}(227, \cdot)\) n/a 11456 8
7752.2.et \(\chi_{7752}(571, \cdot)\) n/a 5184 8
7752.2.eu \(\chi_{7752}(911, \cdot)\) None 0 8
7752.2.ev \(\chi_{7752}(265, \cdot)\) n/a 1440 8
7752.2.ew \(\chi_{7752}(533, \cdot)\) n/a 10368 8
7752.2.fb \(\chi_{7752}(3467, \cdot)\) n/a 8592 6
7752.2.fe \(\chi_{7752}(2789, \cdot)\) n/a 7680 6
7752.2.ff \(\chi_{7752}(679, \cdot)\) None 0 6
7752.2.fg \(\chi_{7752}(815, \cdot)\) None 0 6
7752.2.fh \(\chi_{7752}(613, \cdot)\) n/a 3840 6
7752.2.fk \(\chi_{7752}(67, \cdot)\) n/a 4320 6
7752.2.fl \(\chi_{7752}(545, \cdot)\) n/a 1920 6
7752.2.fq \(\chi_{7752}(307, \cdot)\) n/a 3840 6
7752.2.fr \(\chi_{7752}(713, \cdot)\) n/a 2160 6
7752.2.fu \(\chi_{7752}(1871, \cdot)\) None 0 6
7752.2.fv \(\chi_{7752}(2821, \cdot)\) n/a 4320 6
7752.2.fw \(\chi_{7752}(509, \cdot)\) n/a 8592 6
7752.2.fx \(\chi_{7752}(2143, \cdot)\) None 0 6
7752.2.ga \(\chi_{7752}(169, \cdot)\) n/a 1080 6
7752.2.gb \(\chi_{7752}(35, \cdot)\) n/a 7680 6
7752.2.gi \(\chi_{7752}(559, \cdot)\) None 0 8
7752.2.gj \(\chi_{7752}(977, \cdot)\) n/a 2880 8
7752.2.gk \(\chi_{7752}(83, \cdot)\) n/a 11456 8
7752.2.gl \(\chi_{7752}(349, \cdot)\) n/a 5760 8
7752.2.gm \(\chi_{7752}(331, \cdot)\) n/a 5760 8
7752.2.gn \(\chi_{7752}(1205, \cdot)\) n/a 11456 8
7752.2.go \(\chi_{7752}(695, \cdot)\) None 0 8
7752.2.gp \(\chi_{7752}(49, \cdot)\) n/a 1440 8
7752.2.gu \(\chi_{7752}(319, \cdot)\) None 0 12
7752.2.gx \(\chi_{7752}(251, \cdot)\) n/a 17184 12
7752.2.gz \(\chi_{7752}(625, \cdot)\) n/a 2160 12
7752.2.ha \(\chi_{7752}(965, \cdot)\) n/a 17184 12
7752.2.hc \(\chi_{7752}(157, \cdot)\) n/a 8640 12
7752.2.hf \(\chi_{7752}(89, \cdot)\) n/a 4320 12
7752.2.hh \(\chi_{7752}(523, \cdot)\) n/a 8640 12
7752.2.hi \(\chi_{7752}(47, \cdot)\) None 0 12
7752.2.hm \(\chi_{7752}(601, \cdot)\) n/a 2880 16
7752.2.hn \(\chi_{7752}(125, \cdot)\) n/a 22912 16
7752.2.ho \(\chi_{7752}(163, \cdot)\) n/a 11520 16
7752.2.hp \(\chi_{7752}(335, \cdot)\) None 0 16
7752.2.hu \(\chi_{7752}(7, \cdot)\) None 0 16
7752.2.hv \(\chi_{7752}(107, \cdot)\) n/a 22912 16
7752.2.hw \(\chi_{7752}(445, \cdot)\) n/a 11520 16
7752.2.hx \(\chi_{7752}(809, \cdot)\) n/a 5760 16
7752.2.ib \(\chi_{7752}(25, \cdot)\) n/a 4320 24
7752.2.ic \(\chi_{7752}(355, \cdot)\) n/a 17280 24
7752.2.if \(\chi_{7752}(253, \cdot)\) n/a 17280 24
7752.2.ig \(\chi_{7752}(127, \cdot)\) None 0 24
7752.2.ij \(\chi_{7752}(491, \cdot)\) n/a 34368 24
7752.2.ik \(\chi_{7752}(185, \cdot)\) n/a 8640 24
7752.2.in \(\chi_{7752}(263, \cdot)\) None 0 24
7752.2.io \(\chi_{7752}(53, \cdot)\) n/a 34368 24
7752.2.is \(\chi_{7752}(299, \cdot)\) n/a 68736 48
7752.2.it \(\chi_{7752}(71, \cdot)\) None 0 48
7752.2.iw \(\chi_{7752}(233, \cdot)\) n/a 17280 48
7752.2.ix \(\chi_{7752}(5, \cdot)\) n/a 68736 48
7752.2.iy \(\chi_{7752}(97, \cdot)\) n/a 8640 48
7752.2.iz \(\chi_{7752}(109, \cdot)\) n/a 34560 48
7752.2.jc \(\chi_{7752}(139, \cdot)\) n/a 34560 48
7752.2.jd \(\chi_{7752}(175, \cdot)\) None 0 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7752))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7752)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(323))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(646))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(969))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1292))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1938))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3876))\)\(^{\oplus 2}\)