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Properties

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

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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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(7920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 60}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7920))\)\(^{\oplus 1}\)