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Properties

Label 7440.2
Level 7440
Weight 2
Dimension 567488
Nonzero newspaces 112
Sturm bound 5898240

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Defining parameters

Level: \( N \) = \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(5898240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7440))\).

Total New Old
Modular forms 1488000 570616 917384
Cusp forms 1461121 567488 893633
Eisenstein series 26879 3128 23751

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7440))\)

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
7440.2.a \(\chi_{7440}(1, \cdot)\) 7440.2.a.a 1 1
7440.2.a.b 1
7440.2.a.c 1
7440.2.a.d 1
7440.2.a.e 1
7440.2.a.f 1
7440.2.a.g 1
7440.2.a.h 1
7440.2.a.i 1
7440.2.a.j 1
7440.2.a.k 1
7440.2.a.l 1
7440.2.a.m 1
7440.2.a.n 1
7440.2.a.o 1
7440.2.a.p 1
7440.2.a.q 1
7440.2.a.r 1
7440.2.a.s 1
7440.2.a.t 1
7440.2.a.u 1
7440.2.a.v 1
7440.2.a.w 1
7440.2.a.x 1
7440.2.a.y 1
7440.2.a.z 1
7440.2.a.ba 1
7440.2.a.bb 1
7440.2.a.bc 2
7440.2.a.bd 2
7440.2.a.be 2
7440.2.a.bf 2
7440.2.a.bg 2
7440.2.a.bh 2
7440.2.a.bi 2
7440.2.a.bj 2
7440.2.a.bk 2
7440.2.a.bl 2
7440.2.a.bm 3
7440.2.a.bn 3
7440.2.a.bo 3
7440.2.a.bp 3
7440.2.a.bq 3
7440.2.a.br 3
7440.2.a.bs 3
7440.2.a.bt 3
7440.2.a.bu 3
7440.2.a.bv 3
7440.2.a.bw 3
7440.2.a.bx 4
7440.2.a.by 4
7440.2.a.bz 4
7440.2.a.ca 4
7440.2.a.cb 4
7440.2.a.cc 4
7440.2.a.cd 5
7440.2.a.ce 5
7440.2.a.cf 5
7440.2.b \(\chi_{7440}(4649, \cdot)\) None 0 1
7440.2.c \(\chi_{7440}(311, \cdot)\) None 0 1
7440.2.f \(\chi_{7440}(5209, \cdot)\) None 0 1
7440.2.g \(\chi_{7440}(4711, \cdot)\) None 0 1
7440.2.j \(\chi_{7440}(991, \cdot)\) n/a 128 1
7440.2.k \(\chi_{7440}(1489, \cdot)\) n/a 180 1
7440.2.n \(\chi_{7440}(4031, \cdot)\) n/a 240 1
7440.2.o \(\chi_{7440}(929, \cdot)\) n/a 380 1
7440.2.t \(\chi_{7440}(3721, \cdot)\) None 0 1
7440.2.u \(\chi_{7440}(6199, \cdot)\) None 0 1
7440.2.x \(\chi_{7440}(3161, \cdot)\) None 0 1
7440.2.y \(\chi_{7440}(1799, \cdot)\) None 0 1
7440.2.bb \(\chi_{7440}(5519, \cdot)\) n/a 360 1
7440.2.bc \(\chi_{7440}(6881, \cdot)\) n/a 256 1
7440.2.bf \(\chi_{7440}(2479, \cdot)\) n/a 192 1
7440.2.bg \(\chi_{7440}(3601, \cdot)\) n/a 256 2
7440.2.bl \(\chi_{7440}(1861, \cdot)\) n/a 960 2
7440.2.bm \(\chi_{7440}(1301, \cdot)\) n/a 2048 2
7440.2.bn \(\chi_{7440}(619, \cdot)\) n/a 1536 2
7440.2.bo \(\chi_{7440}(3659, \cdot)\) n/a 2880 2
7440.2.br \(\chi_{7440}(497, \cdot)\) n/a 720 2
7440.2.bs \(\chi_{7440}(433, \cdot)\) n/a 384 2
7440.2.bt \(\chi_{7440}(1487, \cdot)\) n/a 768 2
7440.2.bu \(\chi_{7440}(2047, \cdot)\) n/a 360 2
7440.2.bx \(\chi_{7440}(187, \cdot)\) n/a 1440 2
7440.2.bz \(\chi_{7440}(2293, \cdot)\) n/a 1536 2
7440.2.cc \(\chi_{7440}(2603, \cdot)\) n/a 3056 2
7440.2.ce \(\chi_{7440}(1613, \cdot)\) n/a 2880 2
7440.2.cg \(\chi_{7440}(6013, \cdot)\) n/a 1536 2
7440.2.ci \(\chi_{7440}(3163, \cdot)\) n/a 1440 2
7440.2.cj \(\chi_{7440}(5333, \cdot)\) n/a 2880 2
7440.2.cl \(\chi_{7440}(6323, \cdot)\) n/a 3056 2
7440.2.cp \(\chi_{7440}(743, \cdot)\) None 0 2
7440.2.cq \(\chi_{7440}(1303, \cdot)\) None 0 2
7440.2.cr \(\chi_{7440}(4217, \cdot)\) None 0 2
7440.2.cs \(\chi_{7440}(1177, \cdot)\) None 0 2
7440.2.cv \(\chi_{7440}(2851, \cdot)\) n/a 1024 2
7440.2.cw \(\chi_{7440}(2171, \cdot)\) n/a 1920 2
7440.2.cx \(\chi_{7440}(3349, \cdot)\) n/a 1440 2
7440.2.cy \(\chi_{7440}(2789, \cdot)\) n/a 3056 2
7440.2.dd \(\chi_{7440}(481, \cdot)\) n/a 512 4
7440.2.de \(\chi_{7440}(3199, \cdot)\) n/a 384 2
7440.2.dh \(\chi_{7440}(161, \cdot)\) n/a 512 2
7440.2.di \(\chi_{7440}(1679, \cdot)\) n/a 768 2
7440.2.dl \(\chi_{7440}(1079, \cdot)\) None 0 2
7440.2.dm \(\chi_{7440}(3881, \cdot)\) None 0 2
7440.2.dp \(\chi_{7440}(2599, \cdot)\) None 0 2
7440.2.dq \(\chi_{7440}(3001, \cdot)\) None 0 2
7440.2.dv \(\chi_{7440}(1649, \cdot)\) n/a 760 2
7440.2.dw \(\chi_{7440}(191, \cdot)\) n/a 512 2
7440.2.dz \(\chi_{7440}(769, \cdot)\) n/a 384 2
7440.2.ea \(\chi_{7440}(1711, \cdot)\) n/a 256 2
7440.2.ed \(\chi_{7440}(1111, \cdot)\) None 0 2
7440.2.ee \(\chi_{7440}(1369, \cdot)\) None 0 2
7440.2.eh \(\chi_{7440}(3911, \cdot)\) None 0 2
7440.2.ei \(\chi_{7440}(1049, \cdot)\) None 0 2
7440.2.ej \(\chi_{7440}(1759, \cdot)\) n/a 768 4
7440.2.em \(\chi_{7440}(401, \cdot)\) n/a 1024 4
7440.2.en \(\chi_{7440}(2639, \cdot)\) n/a 1536 4
7440.2.eq \(\chi_{7440}(839, \cdot)\) None 0 4
7440.2.er \(\chi_{7440}(2441, \cdot)\) None 0 4
7440.2.eu \(\chi_{7440}(1639, \cdot)\) None 0 4
7440.2.ev \(\chi_{7440}(841, \cdot)\) None 0 4
7440.2.fa \(\chi_{7440}(209, \cdot)\) n/a 1520 4
7440.2.fb \(\chi_{7440}(1151, \cdot)\) n/a 1024 4
7440.2.fe \(\chi_{7440}(529, \cdot)\) n/a 768 4
7440.2.ff \(\chi_{7440}(271, \cdot)\) n/a 512 4
7440.2.fi \(\chi_{7440}(151, \cdot)\) None 0 4
7440.2.fj \(\chi_{7440}(2329, \cdot)\) None 0 4
7440.2.fm \(\chi_{7440}(791, \cdot)\) None 0 4
7440.2.fn \(\chi_{7440}(89, \cdot)\) None 0 4
7440.2.fs \(\chi_{7440}(1451, \cdot)\) n/a 4096 4
7440.2.ft \(\chi_{7440}(2971, \cdot)\) n/a 2048 4
7440.2.fu \(\chi_{7440}(2909, \cdot)\) n/a 6112 4
7440.2.fv \(\chi_{7440}(2629, \cdot)\) n/a 3072 4
7440.2.fw \(\chi_{7440}(553, \cdot)\) None 0 4
7440.2.fx \(\chi_{7440}(377, \cdot)\) None 0 4
7440.2.gc \(\chi_{7440}(583, \cdot)\) None 0 4
7440.2.gd \(\chi_{7440}(1463, \cdot)\) None 0 4
7440.2.gf \(\chi_{7440}(347, \cdot)\) n/a 6112 4
7440.2.gh \(\chi_{7440}(1493, \cdot)\) n/a 6112 4
7440.2.gi \(\chi_{7440}(67, \cdot)\) n/a 3072 4
7440.2.gk \(\chi_{7440}(37, \cdot)\) n/a 3072 4
7440.2.gm \(\chi_{7440}(893, \cdot)\) n/a 6112 4
7440.2.go \(\chi_{7440}(3323, \cdot)\) n/a 6112 4
7440.2.gr \(\chi_{7440}(3013, \cdot)\) n/a 3072 4
7440.2.gt \(\chi_{7440}(3043, \cdot)\) n/a 3072 4
7440.2.gu \(\chi_{7440}(1183, \cdot)\) n/a 768 4
7440.2.gv \(\chi_{7440}(863, \cdot)\) n/a 1536 4
7440.2.ha \(\chi_{7440}(1153, \cdot)\) n/a 768 4
7440.2.hb \(\chi_{7440}(2753, \cdot)\) n/a 1520 4
7440.2.hc \(\chi_{7440}(1421, \cdot)\) n/a 4096 4
7440.2.hd \(\chi_{7440}(1141, \cdot)\) n/a 2048 4
7440.2.he \(\chi_{7440}(2939, \cdot)\) n/a 6112 4
7440.2.hf \(\chi_{7440}(739, \cdot)\) n/a 3072 4
7440.2.hk \(\chi_{7440}(1681, \cdot)\) n/a 1024 8
7440.2.hp \(\chi_{7440}(29, \cdot)\) n/a 12224 8
7440.2.hq \(\chi_{7440}(109, \cdot)\) n/a 6144 8
7440.2.hr \(\chi_{7440}(1211, \cdot)\) n/a 8192 8
7440.2.hs \(\chi_{7440}(91, \cdot)\) n/a 4096 8
7440.2.hv \(\chi_{7440}(457, \cdot)\) None 0 8
7440.2.hw \(\chi_{7440}(233, \cdot)\) None 0 8
7440.2.hx \(\chi_{7440}(343, \cdot)\) None 0 8
7440.2.hy \(\chi_{7440}(23, \cdot)\) None 0 8
7440.2.ib \(\chi_{7440}(587, \cdot)\) n/a 12224 8
7440.2.id \(\chi_{7440}(2453, \cdot)\) n/a 12224 8
7440.2.ig \(\chi_{7440}(283, \cdot)\) n/a 6144 8
7440.2.ii \(\chi_{7440}(277, \cdot)\) n/a 6144 8
7440.2.ik \(\chi_{7440}(653, \cdot)\) n/a 12224 8
7440.2.im \(\chi_{7440}(1883, \cdot)\) n/a 12224 8
7440.2.in \(\chi_{7440}(1573, \cdot)\) n/a 6144 8
7440.2.ip \(\chi_{7440}(163, \cdot)\) n/a 6144 8
7440.2.it \(\chi_{7440}(1087, \cdot)\) n/a 1536 8
7440.2.iu \(\chi_{7440}(767, \cdot)\) n/a 3072 8
7440.2.iv \(\chi_{7440}(337, \cdot)\) n/a 1536 8
7440.2.iw \(\chi_{7440}(593, \cdot)\) n/a 3040 8
7440.2.iz \(\chi_{7440}(419, \cdot)\) n/a 12224 8
7440.2.ja \(\chi_{7440}(139, \cdot)\) n/a 6144 8
7440.2.jb \(\chi_{7440}(461, \cdot)\) n/a 8192 8
7440.2.jc \(\chi_{7440}(901, \cdot)\) n/a 4096 8
7440.2.jh \(\chi_{7440}(569, \cdot)\) None 0 8
7440.2.ji \(\chi_{7440}(71, \cdot)\) None 0 8
7440.2.jl \(\chi_{7440}(169, \cdot)\) None 0 8
7440.2.jm \(\chi_{7440}(631, \cdot)\) None 0 8
7440.2.jp \(\chi_{7440}(1231, \cdot)\) n/a 1024 8
7440.2.jq \(\chi_{7440}(49, \cdot)\) n/a 1536 8
7440.2.jt \(\chi_{7440}(431, \cdot)\) n/a 2048 8
7440.2.ju \(\chi_{7440}(1169, \cdot)\) n/a 3040 8
7440.2.jz \(\chi_{7440}(121, \cdot)\) None 0 8
7440.2.ka \(\chi_{7440}(199, \cdot)\) None 0 8
7440.2.kd \(\chi_{7440}(761, \cdot)\) None 0 8
7440.2.ke \(\chi_{7440}(359, \cdot)\) None 0 8
7440.2.kh \(\chi_{7440}(479, \cdot)\) n/a 3072 8
7440.2.ki \(\chi_{7440}(641, \cdot)\) n/a 2048 8
7440.2.kl \(\chi_{7440}(79, \cdot)\) n/a 1536 8
7440.2.kq \(\chi_{7440}(259, \cdot)\) n/a 12288 16
7440.2.kr \(\chi_{7440}(59, \cdot)\) n/a 24448 16
7440.2.ks \(\chi_{7440}(421, \cdot)\) n/a 8192 16
7440.2.kt \(\chi_{7440}(941, \cdot)\) n/a 16384 16
7440.2.ku \(\chi_{7440}(113, \cdot)\) n/a 6080 16
7440.2.kv \(\chi_{7440}(673, \cdot)\) n/a 3072 16
7440.2.la \(\chi_{7440}(383, \cdot)\) n/a 6144 16
7440.2.lb \(\chi_{7440}(607, \cdot)\) n/a 3072 16
7440.2.ld \(\chi_{7440}(1123, \cdot)\) n/a 12288 16
7440.2.lf \(\chi_{7440}(613, \cdot)\) n/a 12288 16
7440.2.lg \(\chi_{7440}(203, \cdot)\) n/a 24448 16
7440.2.li \(\chi_{7440}(173, \cdot)\) n/a 24448 16
7440.2.lk \(\chi_{7440}(13, \cdot)\) n/a 12288 16
7440.2.lm \(\chi_{7440}(307, \cdot)\) n/a 12288 16
7440.2.lp \(\chi_{7440}(293, \cdot)\) n/a 24448 16
7440.2.lr \(\chi_{7440}(83, \cdot)\) n/a 24448 16
7440.2.ls \(\chi_{7440}(167, \cdot)\) None 0 16
7440.2.lt \(\chi_{7440}(7, \cdot)\) None 0 16
7440.2.ly \(\chi_{7440}(617, \cdot)\) None 0 16
7440.2.lz \(\chi_{7440}(73, \cdot)\) None 0 16
7440.2.ma \(\chi_{7440}(949, \cdot)\) n/a 12288 16
7440.2.mb \(\chi_{7440}(269, \cdot)\) n/a 24448 16
7440.2.mc \(\chi_{7440}(331, \cdot)\) n/a 8192 16
7440.2.md \(\chi_{7440}(131, \cdot)\) n/a 16384 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(744))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1488))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1860))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3720))\)\(^{\oplus 2}\)