# Properties

 Label 7920.2 Level 7920 Weight 2 Dimension 663686 Nonzero newspaces 112 Sturm bound 6635520

## Defining parameters

 Level: $$N$$ = $$7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$112$$ Sturm bound: $$6635520$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7920))$$.

Total New Old
Modular forms 1676800 668062 1008738
Cusp forms 1640961 663686 977275
Eisenstein series 35839 4376 31463

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7920))$$

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
7920.2.a $$\chi_{7920}(1, \cdot)$$ 7920.2.a.a 1 1
7920.2.a.b 1
7920.2.a.c 1
7920.2.a.d 1
7920.2.a.e 1
7920.2.a.f 1
7920.2.a.g 1
7920.2.a.h 1
7920.2.a.i 1
7920.2.a.j 1
7920.2.a.k 1
7920.2.a.l 1
7920.2.a.m 1
7920.2.a.n 1
7920.2.a.o 1
7920.2.a.p 1
7920.2.a.q 1
7920.2.a.r 1
7920.2.a.s 1
7920.2.a.t 1
7920.2.a.u 1
7920.2.a.v 1
7920.2.a.w 1
7920.2.a.x 1
7920.2.a.y 1
7920.2.a.z 1
7920.2.a.ba 1
7920.2.a.bb 1
7920.2.a.bc 1
7920.2.a.bd 1
7920.2.a.be 1
7920.2.a.bf 1
7920.2.a.bg 1
7920.2.a.bh 1
7920.2.a.bi 1
7920.2.a.bj 1
7920.2.a.bk 1
7920.2.a.bl 1
7920.2.a.bm 1
7920.2.a.bn 2
7920.2.a.bo 2
7920.2.a.bp 2
7920.2.a.bq 2
7920.2.a.br 2
7920.2.a.bs 2
7920.2.a.bt 2
7920.2.a.bu 2
7920.2.a.bv 2
7920.2.a.bw 2
7920.2.a.bx 2
7920.2.a.by 2
7920.2.a.bz 2
7920.2.a.ca 2
7920.2.a.cb 2
7920.2.a.cc 2
7920.2.a.cd 2
7920.2.a.ce 2
7920.2.a.cf 2
7920.2.a.cg 2
7920.2.a.ch 2
7920.2.a.ci 2
7920.2.a.cj 3
7920.2.a.ck 3
7920.2.a.cl 3
7920.2.a.cm 4
7920.2.a.cn 4
7920.2.d $$\chi_{7920}(3169, \cdot)$$ n/a 150 1
7920.2.e $$\chi_{7920}(5831, \cdot)$$ None 0 1
7920.2.f $$\chi_{7920}(3761, \cdot)$$ 7920.2.f.a 8 1
7920.2.f.b 8
7920.2.f.c 12
7920.2.f.d 12
7920.2.f.e 12
7920.2.f.f 12
7920.2.f.g 16
7920.2.f.h 16
7920.2.g $$\chi_{7920}(3079, \cdot)$$ None 0 1
7920.2.j $$\chi_{7920}(7129, \cdot)$$ None 0 1
7920.2.k $$\chi_{7920}(1871, \cdot)$$ 7920.2.k.a 16 1
7920.2.k.b 16
7920.2.k.c 24
7920.2.k.d 24
7920.2.p $$\chi_{7920}(7721, \cdot)$$ None 0 1
7920.2.q $$\chi_{7920}(7039, \cdot)$$ n/a 180 1
7920.2.t $$\chi_{7920}(3871, \cdot)$$ n/a 120 1
7920.2.u $$\chi_{7920}(2969, \cdot)$$ None 0 1
7920.2.v $$\chi_{7920}(5039, \cdot)$$ n/a 120 1
7920.2.w $$\chi_{7920}(3961, \cdot)$$ None 0 1
7920.2.z $$\chi_{7920}(7831, \cdot)$$ None 0 1
7920.2.ba $$\chi_{7920}(6929, \cdot)$$ n/a 144 1
7920.2.bf $$\chi_{7920}(1079, \cdot)$$ None 0 1
7920.2.bg $$\chi_{7920}(2641, \cdot)$$ n/a 480 2
7920.2.bi $$\chi_{7920}(989, \cdot)$$ n/a 1152 2
7920.2.bj $$\chi_{7920}(1891, \cdot)$$ n/a 960 2
7920.2.bm $$\chi_{7920}(1981, \cdot)$$ n/a 800 2
7920.2.bn $$\chi_{7920}(3059, \cdot)$$ n/a 960 2
7920.2.bp $$\chi_{7920}(1387, \cdot)$$ n/a 1200 2
7920.2.br $$\chi_{7920}(1187, \cdot)$$ n/a 1152 2
7920.2.bu $$\chi_{7920}(5237, \cdot)$$ n/a 960 2
7920.2.bw $$\chi_{7920}(3277, \cdot)$$ n/a 1432 2
7920.2.by $$\chi_{7920}(1583, \cdot)$$ n/a 288 2
7920.2.bz $$\chi_{7920}(3673, \cdot)$$ None 0 2
7920.2.cc $$\chi_{7920}(1783, \cdot)$$ None 0 2
7920.2.cd $$\chi_{7920}(5633, \cdot)$$ n/a 240 2
7920.2.cg $$\chi_{7920}(5743, \cdot)$$ n/a 300 2
7920.2.ch $$\chi_{7920}(1673, \cdot)$$ None 0 2
7920.2.ck $$\chi_{7920}(5543, \cdot)$$ None 0 2
7920.2.cl $$\chi_{7920}(1297, \cdot)$$ n/a 356 2
7920.2.cn $$\chi_{7920}(5147, \cdot)$$ n/a 1152 2
7920.2.cp $$\chi_{7920}(5347, \cdot)$$ n/a 1200 2
7920.2.cs $$\chi_{7920}(1693, \cdot)$$ n/a 1432 2
7920.2.cu $$\chi_{7920}(1277, \cdot)$$ n/a 960 2
7920.2.cv $$\chi_{7920}(3851, \cdot)$$ n/a 640 2
7920.2.cy $$\chi_{7920}(1189, \cdot)$$ n/a 1200 2
7920.2.cz $$\chi_{7920}(1099, \cdot)$$ n/a 1432 2
7920.2.dc $$\chi_{7920}(1781, \cdot)$$ n/a 768 2
7920.2.dd $$\chi_{7920}(2161, \cdot)$$ n/a 480 4
7920.2.de $$\chi_{7920}(1649, \cdot)$$ n/a 856 2
7920.2.df $$\chi_{7920}(2551, \cdot)$$ None 0 2
7920.2.dk $$\chi_{7920}(3719, \cdot)$$ None 0 2
7920.2.dn $$\chi_{7920}(329, \cdot)$$ None 0 2
7920.2.do $$\chi_{7920}(1231, \cdot)$$ n/a 576 2
7920.2.dp $$\chi_{7920}(1321, \cdot)$$ None 0 2
7920.2.dq $$\chi_{7920}(2399, \cdot)$$ n/a 720 2
7920.2.dt $$\chi_{7920}(4511, \cdot)$$ n/a 480 2
7920.2.du $$\chi_{7920}(1849, \cdot)$$ None 0 2
7920.2.dz $$\chi_{7920}(1759, \cdot)$$ n/a 864 2
7920.2.ea $$\chi_{7920}(2441, \cdot)$$ None 0 2
7920.2.ed $$\chi_{7920}(551, \cdot)$$ None 0 2
7920.2.ee $$\chi_{7920}(529, \cdot)$$ n/a 720 2
7920.2.ef $$\chi_{7920}(439, \cdot)$$ None 0 2
7920.2.eg $$\chi_{7920}(1121, \cdot)$$ n/a 576 2
7920.2.ej $$\chi_{7920}(3239, \cdot)$$ None 0 4
7920.2.eo $$\chi_{7920}(2791, \cdot)$$ None 0 4
7920.2.ep $$\chi_{7920}(1889, \cdot)$$ n/a 576 4
7920.2.es $$\chi_{7920}(719, \cdot)$$ n/a 576 4
7920.2.et $$\chi_{7920}(361, \cdot)$$ None 0 4
7920.2.eu $$\chi_{7920}(271, \cdot)$$ n/a 480 4
7920.2.ev $$\chi_{7920}(809, \cdot)$$ None 0 4
7920.2.ey $$\chi_{7920}(2681, \cdot)$$ None 0 4
7920.2.ez $$\chi_{7920}(1999, \cdot)$$ n/a 720 4
7920.2.fe $$\chi_{7920}(1369, \cdot)$$ None 0 4
7920.2.ff $$\chi_{7920}(4031, \cdot)$$ n/a 384 4
7920.2.fi $$\chi_{7920}(161, \cdot)$$ n/a 384 4
7920.2.fj $$\chi_{7920}(919, \cdot)$$ None 0 4
7920.2.fk $$\chi_{7920}(289, \cdot)$$ n/a 712 4
7920.2.fl $$\chi_{7920}(71, \cdot)$$ None 0 4
7920.2.fo $$\chi_{7920}(2509, \cdot)$$ n/a 5760 4
7920.2.fr $$\chi_{7920}(1211, \cdot)$$ n/a 3840 4
7920.2.fs $$\chi_{7920}(461, \cdot)$$ n/a 4608 4
7920.2.fv $$\chi_{7920}(2419, \cdot)$$ n/a 6880 4
7920.2.fw $$\chi_{7920}(1957, \cdot)$$ n/a 6880 4
7920.2.fy $$\chi_{7920}(1013, \cdot)$$ n/a 5760 4
7920.2.gb $$\chi_{7920}(2243, \cdot)$$ n/a 6880 4
7920.2.gd $$\chi_{7920}(67, \cdot)$$ n/a 5760 4
7920.2.gf $$\chi_{7920}(353, \cdot)$$ n/a 1440 4
7920.2.gg $$\chi_{7920}(727, \cdot)$$ None 0 4
7920.2.gj $$\chi_{7920}(1033, \cdot)$$ None 0 4
7920.2.gk $$\chi_{7920}(527, \cdot)$$ n/a 1728 4
7920.2.gn $$\chi_{7920}(2353, \cdot)$$ n/a 1712 4
7920.2.go $$\chi_{7920}(263, \cdot)$$ None 0 4
7920.2.gr $$\chi_{7920}(617, \cdot)$$ None 0 4
7920.2.gs $$\chi_{7920}(463, \cdot)$$ n/a 1440 4
7920.2.gu $$\chi_{7920}(2333, \cdot)$$ n/a 5760 4
7920.2.gw $$\chi_{7920}(373, \cdot)$$ n/a 6880 4
7920.2.gz $$\chi_{7920}(1123, \cdot)$$ n/a 5760 4
7920.2.hb $$\chi_{7920}(923, \cdot)$$ n/a 6880 4
7920.2.hd $$\chi_{7920}(571, \cdot)$$ n/a 4608 4
7920.2.he $$\chi_{7920}(2309, \cdot)$$ n/a 6880 4
7920.2.hh $$\chi_{7920}(419, \cdot)$$ n/a 5760 4
7920.2.hi $$\chi_{7920}(661, \cdot)$$ n/a 3840 4
7920.2.hk $$\chi_{7920}(961, \cdot)$$ n/a 2304 8
7920.2.hm $$\chi_{7920}(19, \cdot)$$ n/a 5728 8
7920.2.hn $$\chi_{7920}(701, \cdot)$$ n/a 3072 8
7920.2.hq $$\chi_{7920}(251, \cdot)$$ n/a 3072 8
7920.2.hr $$\chi_{7920}(829, \cdot)$$ n/a 5728 8
7920.2.ht $$\chi_{7920}(53, \cdot)$$ n/a 4608 8
7920.2.hv $$\chi_{7920}(2197, \cdot)$$ n/a 5728 8
7920.2.hy $$\chi_{7920}(1027, \cdot)$$ n/a 5728 8
7920.2.ia $$\chi_{7920}(107, \cdot)$$ n/a 4608 8
7920.2.ic $$\chi_{7920}(2593, \cdot)$$ n/a 1424 8
7920.2.id $$\chi_{7920}(503, \cdot)$$ None 0 8
7920.2.ig $$\chi_{7920}(377, \cdot)$$ None 0 8
7920.2.ih $$\chi_{7920}(1423, \cdot)$$ n/a 1440 8
7920.2.ik $$\chi_{7920}(1313, \cdot)$$ n/a 1152 8
7920.2.il $$\chi_{7920}(487, \cdot)$$ None 0 8
7920.2.io $$\chi_{7920}(73, \cdot)$$ None 0 8
7920.2.ip $$\chi_{7920}(1007, \cdot)$$ n/a 1152 8
7920.2.ir $$\chi_{7920}(613, \cdot)$$ n/a 5728 8
7920.2.it $$\chi_{7920}(917, \cdot)$$ n/a 4608 8
7920.2.iw $$\chi_{7920}(1403, \cdot)$$ n/a 4608 8
7920.2.iy $$\chi_{7920}(163, \cdot)$$ n/a 5728 8
7920.2.iz $$\chi_{7920}(181, \cdot)$$ n/a 3840 8
7920.2.jc $$\chi_{7920}(179, \cdot)$$ n/a 4608 8
7920.2.jd $$\chi_{7920}(629, \cdot)$$ n/a 4608 8
7920.2.jg $$\chi_{7920}(811, \cdot)$$ n/a 3840 8
7920.2.jj $$\chi_{7920}(679, \cdot)$$ None 0 8
7920.2.jk $$\chi_{7920}(1361, \cdot)$$ n/a 2304 8
7920.2.jl $$\chi_{7920}(311, \cdot)$$ None 0 8
7920.2.jm $$\chi_{7920}(49, \cdot)$$ n/a 3424 8
7920.2.jp $$\chi_{7920}(79, \cdot)$$ n/a 3456 8
7920.2.jq $$\chi_{7920}(41, \cdot)$$ None 0 8
7920.2.jv $$\chi_{7920}(191, \cdot)$$ n/a 2304 8
7920.2.jw $$\chi_{7920}(169, \cdot)$$ None 0 8
7920.2.jz $$\chi_{7920}(841, \cdot)$$ None 0 8
7920.2.ka $$\chi_{7920}(1919, \cdot)$$ n/a 3456 8
7920.2.kb $$\chi_{7920}(569, \cdot)$$ None 0 8
7920.2.kc $$\chi_{7920}(1471, \cdot)$$ n/a 2304 8
7920.2.kf $$\chi_{7920}(119, \cdot)$$ None 0 8
7920.2.kk $$\chi_{7920}(689, \cdot)$$ n/a 3424 8
7920.2.kl $$\chi_{7920}(151, \cdot)$$ None 0 8
7920.2.km $$\chi_{7920}(59, \cdot)$$ n/a 27520 16
7920.2.kp $$\chi_{7920}(301, \cdot)$$ n/a 18432 16
7920.2.kq $$\chi_{7920}(211, \cdot)$$ n/a 18432 16
7920.2.kt $$\chi_{7920}(29, \cdot)$$ n/a 27520 16
7920.2.ku $$\chi_{7920}(227, \cdot)$$ n/a 27520 16
7920.2.kw $$\chi_{7920}(427, \cdot)$$ n/a 27520 16
7920.2.kz $$\chi_{7920}(853, \cdot)$$ n/a 27520 16
7920.2.lb $$\chi_{7920}(653, \cdot)$$ n/a 27520 16
7920.2.ld $$\chi_{7920}(223, \cdot)$$ n/a 6912 16
7920.2.le $$\chi_{7920}(137, \cdot)$$ None 0 16
7920.2.lh $$\chi_{7920}(167, \cdot)$$ None 0 16
7920.2.li $$\chi_{7920}(193, \cdot)$$ n/a 6848 16
7920.2.ll $$\chi_{7920}(623, \cdot)$$ n/a 6912 16
7920.2.lm $$\chi_{7920}(457, \cdot)$$ None 0 16
7920.2.lp $$\chi_{7920}(103, \cdot)$$ None 0 16
7920.2.lq $$\chi_{7920}(113, \cdot)$$ n/a 6848 16
7920.2.ls $$\chi_{7920}(763, \cdot)$$ n/a 27520 16
7920.2.lu $$\chi_{7920}(83, \cdot)$$ n/a 27520 16
7920.2.lx $$\chi_{7920}(317, \cdot)$$ n/a 27520 16
7920.2.lz $$\chi_{7920}(13, \cdot)$$ n/a 27520 16
7920.2.mb $$\chi_{7920}(101, \cdot)$$ n/a 18432 16
7920.2.mc $$\chi_{7920}(139, \cdot)$$ n/a 27520 16
7920.2.mf $$\chi_{7920}(229, \cdot)$$ n/a 27520 16
7920.2.mg $$\chi_{7920}(731, \cdot)$$ n/a 18432 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7920))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7920)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(330))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(396))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(495))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(528))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(660))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(720))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(792))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(880))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(990))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1320))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1584))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1980))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2640))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3960))$$$$^{\oplus 2}$$