# Properties

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

## 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

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