Properties

Label 7524.2
Level 7524
Weight 2
Dimension 699556
Nonzero newspaces 128
Sturm bound 6220800

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Defining parameters

Level: \( N \) = \( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 128 \)
Sturm bound: \(6220800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7524))\).

Total New Old
Modular forms 1569600 705060 864540
Cusp forms 1540801 699556 841245
Eisenstein series 28799 5504 23295

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7524))\)

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
7524.2.a \(\chi_{7524}(1, \cdot)\) 7524.2.a.a 1 1
7524.2.a.b 1
7524.2.a.c 1
7524.2.a.d 1
7524.2.a.e 1
7524.2.a.f 1
7524.2.a.g 1
7524.2.a.h 2
7524.2.a.i 3
7524.2.a.j 3
7524.2.a.k 3
7524.2.a.l 3
7524.2.a.m 3
7524.2.a.n 4
7524.2.a.o 4
7524.2.a.p 4
7524.2.a.q 6
7524.2.a.r 6
7524.2.a.s 7
7524.2.a.t 7
7524.2.a.u 7
7524.2.a.v 7
7524.2.c \(\chi_{7524}(989, \cdot)\) 7524.2.c.a 72 1
7524.2.d \(\chi_{7524}(5435, \cdot)\) n/a 360 1
7524.2.f \(\chi_{7524}(4445, \cdot)\) 7524.2.f.a 64 1
7524.2.i \(\chi_{7524}(7523, \cdot)\) n/a 480 1
7524.2.k \(\chi_{7524}(6535, \cdot)\) n/a 500 1
7524.2.l \(\chi_{7524}(2089, \cdot)\) 7524.2.l.a 4 1
7524.2.l.b 8
7524.2.l.c 8
7524.2.l.d 16
7524.2.l.e 24
7524.2.l.f 40
7524.2.n \(\chi_{7524}(3079, \cdot)\) n/a 540 1
7524.2.q \(\chi_{7524}(2509, \cdot)\) n/a 360 2
7524.2.r \(\chi_{7524}(1717, \cdot)\) n/a 400 2
7524.2.s \(\chi_{7524}(1189, \cdot)\) n/a 164 2
7524.2.t \(\chi_{7524}(3697, \cdot)\) n/a 400 2
7524.2.u \(\chi_{7524}(685, \cdot)\) n/a 360 4
7524.2.v \(\chi_{7524}(3299, \cdot)\) n/a 2864 2
7524.2.y \(\chi_{7524}(221, \cdot)\) n/a 400 2
7524.2.ba \(\chi_{7524}(4115, \cdot)\) n/a 2400 2
7524.2.bb \(\chi_{7524}(2705, \cdot)\) n/a 480 2
7524.2.be \(\chi_{7524}(901, \cdot)\) n/a 200 2
7524.2.bf \(\chi_{7524}(5347, \cdot)\) n/a 1000 2
7524.2.bi \(\chi_{7524}(1759, \cdot)\) n/a 2864 2
7524.2.bk \(\chi_{7524}(571, \cdot)\) n/a 2592 2
7524.2.bn \(\chi_{7524}(2311, \cdot)\) n/a 2400 2
7524.2.bp \(\chi_{7524}(4597, \cdot)\) n/a 480 2
7524.2.bs \(\chi_{7524}(1519, \cdot)\) n/a 2400 2
7524.2.bu \(\chi_{7524}(5389, \cdot)\) n/a 480 2
7524.2.bx \(\chi_{7524}(2287, \cdot)\) n/a 1192 2
7524.2.bz \(\chi_{7524}(4643, \cdot)\) n/a 800 2
7524.2.ca \(\chi_{7524}(197, \cdot)\) n/a 160 2
7524.2.cd \(\chi_{7524}(2729, \cdot)\) n/a 400 2
7524.2.cf \(\chi_{7524}(2507, \cdot)\) n/a 2864 2
7524.2.cg \(\chi_{7524}(1937, \cdot)\) n/a 400 2
7524.2.ci \(\chi_{7524}(1319, \cdot)\) n/a 2864 2
7524.2.ck \(\chi_{7524}(4685, \cdot)\) n/a 480 2
7524.2.cm \(\chi_{7524}(419, \cdot)\) n/a 2160 2
7524.2.cp \(\chi_{7524}(3497, \cdot)\) n/a 432 2
7524.2.cr \(\chi_{7524}(1607, \cdot)\) n/a 2400 2
7524.2.cs \(\chi_{7524}(791, \cdot)\) n/a 960 2
7524.2.cv \(\chi_{7524}(3257, \cdot)\) n/a 128 2
7524.2.cy \(\chi_{7524}(6775, \cdot)\) n/a 2864 2
7524.2.da \(\chi_{7524}(373, \cdot)\) n/a 480 2
7524.2.db \(\chi_{7524}(331, \cdot)\) n/a 2400 2
7524.2.dd \(\chi_{7524}(397, \cdot)\) n/a 504 6
7524.2.de \(\chi_{7524}(2113, \cdot)\) n/a 1200 6
7524.2.df \(\chi_{7524}(529, \cdot)\) n/a 1200 6
7524.2.di \(\chi_{7524}(343, \cdot)\) n/a 2160 4
7524.2.dk \(\chi_{7524}(721, \cdot)\) n/a 400 4
7524.2.dl \(\chi_{7524}(379, \cdot)\) n/a 2384 4
7524.2.dn \(\chi_{7524}(2735, \cdot)\) n/a 1920 4
7524.2.dq \(\chi_{7524}(1709, \cdot)\) n/a 320 4
7524.2.ds \(\chi_{7524}(647, \cdot)\) n/a 1728 4
7524.2.dt \(\chi_{7524}(305, \cdot)\) n/a 288 4
7524.2.dv \(\chi_{7524}(961, \cdot)\) n/a 1920 8
7524.2.dw \(\chi_{7524}(577, \cdot)\) n/a 800 8
7524.2.dx \(\chi_{7524}(49, \cdot)\) n/a 1920 8
7524.2.dy \(\chi_{7524}(229, \cdot)\) n/a 1728 8
7524.2.ea \(\chi_{7524}(67, \cdot)\) n/a 7200 6
7524.2.eb \(\chi_{7524}(329, \cdot)\) n/a 1440 6
7524.2.ed \(\chi_{7524}(2617, \cdot)\) n/a 1440 6
7524.2.eg \(\chi_{7524}(23, \cdot)\) n/a 7200 6
7524.2.ei \(\chi_{7524}(1409, \cdot)\) n/a 1200 6
7524.2.ej \(\chi_{7524}(967, \cdot)\) n/a 8592 6
7524.2.em \(\chi_{7524}(395, \cdot)\) n/a 2880 6
7524.2.eo \(\chi_{7524}(89, \cdot)\) n/a 408 6
7524.2.er \(\chi_{7524}(1099, \cdot)\) n/a 3576 6
7524.2.es \(\chi_{7524}(527, \cdot)\) n/a 8592 6
7524.2.ew \(\chi_{7524}(241, \cdot)\) n/a 1440 6
7524.2.ex \(\chi_{7524}(815, \cdot)\) n/a 7200 6
7524.2.fa \(\chi_{7524}(991, \cdot)\) n/a 3000 6
7524.2.fb \(\chi_{7524}(593, \cdot)\) n/a 480 6
7524.2.fd \(\chi_{7524}(109, \cdot)\) n/a 600 6
7524.2.fg \(\chi_{7524}(1871, \cdot)\) n/a 2400 6
7524.2.fh \(\chi_{7524}(1915, \cdot)\) n/a 7200 6
7524.2.fk \(\chi_{7524}(1517, \cdot)\) n/a 1440 6
7524.2.fm \(\chi_{7524}(2903, \cdot)\) n/a 8592 6
7524.2.fo \(\chi_{7524}(1541, \cdot)\) n/a 1200 6
7524.2.fr \(\chi_{7524}(43, \cdot)\) n/a 8592 6
7524.2.ft \(\chi_{7524}(31, \cdot)\) n/a 11456 8
7524.2.fu \(\chi_{7524}(673, \cdot)\) n/a 1920 8
7524.2.fw \(\chi_{7524}(1987, \cdot)\) n/a 11456 8
7524.2.fz \(\chi_{7524}(449, \cdot)\) n/a 640 8
7524.2.gc \(\chi_{7524}(107, \cdot)\) n/a 3840 8
7524.2.gd \(\chi_{7524}(2291, \cdot)\) n/a 11456 8
7524.2.gf \(\chi_{7524}(761, \cdot)\) n/a 1728 8
7524.2.gi \(\chi_{7524}(191, \cdot)\) n/a 10368 8
7524.2.gk \(\chi_{7524}(425, \cdot)\) n/a 1920 8
7524.2.gm \(\chi_{7524}(635, \cdot)\) n/a 11456 8
7524.2.go \(\chi_{7524}(113, \cdot)\) n/a 1920 8
7524.2.gp \(\chi_{7524}(227, \cdot)\) n/a 11456 8
7524.2.gr \(\chi_{7524}(977, \cdot)\) n/a 1920 8
7524.2.gu \(\chi_{7524}(809, \cdot)\) n/a 640 8
7524.2.gv \(\chi_{7524}(467, \cdot)\) n/a 3840 8
7524.2.gx \(\chi_{7524}(919, \cdot)\) n/a 4768 8
7524.2.ha \(\chi_{7524}(601, \cdot)\) n/a 1920 8
7524.2.hc \(\chi_{7524}(1291, \cdot)\) n/a 11456 8
7524.2.hf \(\chi_{7524}(1861, \cdot)\) n/a 1920 8
7524.2.hh \(\chi_{7524}(103, \cdot)\) n/a 11456 8
7524.2.hk \(\chi_{7524}(799, \cdot)\) n/a 10368 8
7524.2.hm \(\chi_{7524}(7, \cdot)\) n/a 11456 8
7524.2.hp \(\chi_{7524}(487, \cdot)\) n/a 4768 8
7524.2.hq \(\chi_{7524}(145, \cdot)\) n/a 800 8
7524.2.ht \(\chi_{7524}(1337, \cdot)\) n/a 1920 8
7524.2.hu \(\chi_{7524}(311, \cdot)\) n/a 11456 8
7524.2.hw \(\chi_{7524}(905, \cdot)\) n/a 1920 8
7524.2.hz \(\chi_{7524}(563, \cdot)\) n/a 11456 8
7524.2.ia \(\chi_{7524}(169, \cdot)\) n/a 5760 24
7524.2.ib \(\chi_{7524}(25, \cdot)\) n/a 5760 24
7524.2.ic \(\chi_{7524}(289, \cdot)\) n/a 2400 24
7524.2.ie \(\chi_{7524}(139, \cdot)\) n/a 34368 24
7524.2.if \(\chi_{7524}(257, \cdot)\) n/a 5760 24
7524.2.ij \(\chi_{7524}(167, \cdot)\) n/a 34368 24
7524.2.il \(\chi_{7524}(101, \cdot)\) n/a 5760 24
7524.2.im \(\chi_{7524}(295, \cdot)\) n/a 34368 24
7524.2.ip \(\chi_{7524}(251, \cdot)\) n/a 11520 24
7524.2.iq \(\chi_{7524}(325, \cdot)\) n/a 2400 24
7524.2.is \(\chi_{7524}(17, \cdot)\) n/a 1920 24
7524.2.iv \(\chi_{7524}(91, \cdot)\) n/a 14304 24
7524.2.iw \(\chi_{7524}(47, \cdot)\) n/a 34368 24
7524.2.iz \(\chi_{7524}(193, \cdot)\) n/a 5760 24
7524.2.jb \(\chi_{7524}(371, \cdot)\) n/a 34368 24
7524.2.je \(\chi_{7524}(271, \cdot)\) n/a 14304 24
7524.2.jf \(\chi_{7524}(53, \cdot)\) n/a 1920 24
7524.2.jj \(\chi_{7524}(431, \cdot)\) n/a 11520 24
7524.2.jk \(\chi_{7524}(283, \cdot)\) n/a 34368 24
7524.2.jn \(\chi_{7524}(185, \cdot)\) n/a 5760 24
7524.2.jp \(\chi_{7524}(119, \cdot)\) n/a 34368 24
7524.2.jq \(\chi_{7524}(13, \cdot)\) n/a 5760 24
7524.2.js \(\chi_{7524}(365, \cdot)\) n/a 5760 24
7524.2.jv \(\chi_{7524}(223, \cdot)\) n/a 34368 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7524))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7524)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(836))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1254))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1881))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2508))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3762))\)\(^{\oplus 2}\)