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Properties

Label 7840.2
Level 7840
Weight 2
Dimension 890862
Nonzero newspaces 80
Sturm bound 7225344

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Defining parameters

Level: \( N \) = \( 7840 = 2^{5} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(7225344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7840))\).

Total New Old
Modular forms 1821696 896682 925014
Cusp forms 1790977 890862 900115
Eisenstein series 30719 5820 24899

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7840))\)

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
7840.2.a \(\chi_{7840}(1, \cdot)\) 7840.2.a.a 1 1
7840.2.a.b 1
7840.2.a.c 1
7840.2.a.d 1
7840.2.a.e 1
7840.2.a.f 1
7840.2.a.g 1
7840.2.a.h 1
7840.2.a.i 1
7840.2.a.j 1
7840.2.a.k 1
7840.2.a.l 1
7840.2.a.m 1
7840.2.a.n 1
7840.2.a.o 1
7840.2.a.p 1
7840.2.a.q 1
7840.2.a.r 1
7840.2.a.s 1
7840.2.a.t 1
7840.2.a.u 1
7840.2.a.v 1
7840.2.a.w 1
7840.2.a.x 1
7840.2.a.y 1
7840.2.a.z 1
7840.2.a.ba 2
7840.2.a.bb 2
7840.2.a.bc 2
7840.2.a.bd 2
7840.2.a.be 2
7840.2.a.bf 2
7840.2.a.bg 2
7840.2.a.bh 2
7840.2.a.bi 2
7840.2.a.bj 2
7840.2.a.bk 2
7840.2.a.bl 3
7840.2.a.bm 3
7840.2.a.bn 3
7840.2.a.bo 3
7840.2.a.bp 4
7840.2.a.bq 4
7840.2.a.br 4
7840.2.a.bs 4
7840.2.a.bt 4
7840.2.a.bu 4
7840.2.a.bv 4
7840.2.a.bw 4
7840.2.a.bx 5
7840.2.a.by 5
7840.2.a.bz 5
7840.2.a.ca 5
7840.2.a.cb 6
7840.2.a.cc 6
7840.2.a.cd 6
7840.2.a.ce 6
7840.2.a.cf 6
7840.2.a.cg 6
7840.2.a.ch 8
7840.2.a.ci 8
7840.2.b \(\chi_{7840}(3921, \cdot)\) n/a 164 1
7840.2.e \(\chi_{7840}(7839, \cdot)\) n/a 240 1
7840.2.g \(\chi_{7840}(1569, \cdot)\) n/a 246 1
7840.2.h \(\chi_{7840}(2351, \cdot)\) n/a 160 1
7840.2.k \(\chi_{7840}(6271, \cdot)\) n/a 160 1
7840.2.l \(\chi_{7840}(5489, \cdot)\) n/a 236 1
7840.2.n \(\chi_{7840}(3919, \cdot)\) n/a 232 1
7840.2.q \(\chi_{7840}(961, \cdot)\) n/a 320 2
7840.2.r \(\chi_{7840}(1273, \cdot)\) None 0 2
7840.2.t \(\chi_{7840}(1863, \cdot)\) None 0 2
7840.2.w \(\chi_{7840}(4017, \cdot)\) n/a 464 2
7840.2.x \(\chi_{7840}(4607, \cdot)\) n/a 492 2
7840.2.bb \(\chi_{7840}(3529, \cdot)\) None 0 2
7840.2.bc \(\chi_{7840}(391, \cdot)\) None 0 2
7840.2.bd \(\chi_{7840}(1961, \cdot)\) None 0 2
7840.2.be \(\chi_{7840}(1959, \cdot)\) None 0 2
7840.2.bi \(\chi_{7840}(687, \cdot)\) n/a 472 2
7840.2.bj \(\chi_{7840}(97, \cdot)\) n/a 480 2
7840.2.bl \(\chi_{7840}(5783, \cdot)\) None 0 2
7840.2.bn \(\chi_{7840}(5193, \cdot)\) None 0 2
7840.2.bq \(\chi_{7840}(2959, \cdot)\) n/a 464 2
7840.2.bs \(\chi_{7840}(31, \cdot)\) n/a 320 2
7840.2.bv \(\chi_{7840}(3889, \cdot)\) n/a 464 2
7840.2.bw \(\chi_{7840}(2529, \cdot)\) n/a 480 2
7840.2.bz \(\chi_{7840}(1391, \cdot)\) n/a 320 2
7840.2.cb \(\chi_{7840}(2321, \cdot)\) n/a 320 2
7840.2.cc \(\chi_{7840}(1599, \cdot)\) n/a 480 2
7840.2.ce \(\chi_{7840}(1121, \cdot)\) n/a 1344 6
7840.2.ch \(\chi_{7840}(981, \cdot)\) n/a 2624 4
7840.2.ci \(\chi_{7840}(979, \cdot)\) n/a 3808 4
7840.2.cj \(\chi_{7840}(1077, \cdot)\) n/a 3808 4
7840.2.ck \(\chi_{7840}(1667, \cdot)\) n/a 3896 4
7840.2.cn \(\chi_{7840}(883, \cdot)\) n/a 3896 4
7840.2.co \(\chi_{7840}(293, \cdot)\) n/a 3808 4
7840.2.ct \(\chi_{7840}(1371, \cdot)\) n/a 2560 4
7840.2.cu \(\chi_{7840}(589, \cdot)\) n/a 3896 4
7840.2.cw \(\chi_{7840}(4183, \cdot)\) None 0 4
7840.2.cy \(\chi_{7840}(4233, \cdot)\) None 0 4
7840.2.cz \(\chi_{7840}(1697, \cdot)\) n/a 960 4
7840.2.dc \(\chi_{7840}(1647, \cdot)\) n/a 928 4
7840.2.df \(\chi_{7840}(999, \cdot)\) None 0 4
7840.2.dg \(\chi_{7840}(361, \cdot)\) None 0 4
7840.2.dh \(\chi_{7840}(1991, \cdot)\) None 0 4
7840.2.di \(\chi_{7840}(569, \cdot)\) None 0 4
7840.2.dl \(\chi_{7840}(863, \cdot)\) n/a 960 4
7840.2.do \(\chi_{7840}(913, \cdot)\) n/a 928 4
7840.2.dq \(\chi_{7840}(313, \cdot)\) None 0 4
7840.2.ds \(\chi_{7840}(263, \cdot)\) None 0 4
7840.2.du \(\chi_{7840}(559, \cdot)\) n/a 1992 6
7840.2.dw \(\chi_{7840}(1009, \cdot)\) n/a 1992 6
7840.2.dz \(\chi_{7840}(671, \cdot)\) n/a 1344 6
7840.2.ea \(\chi_{7840}(111, \cdot)\) n/a 1344 6
7840.2.ed \(\chi_{7840}(449, \cdot)\) n/a 2016 6
7840.2.ef \(\chi_{7840}(1119, \cdot)\) n/a 2016 6
7840.2.eg \(\chi_{7840}(561, \cdot)\) n/a 1344 6
7840.2.ei \(\chi_{7840}(641, \cdot)\) n/a 2688 12
7840.2.ej \(\chi_{7840}(949, \cdot)\) n/a 7616 8
7840.2.ek \(\chi_{7840}(411, \cdot)\) n/a 5120 8
7840.2.ep \(\chi_{7840}(667, \cdot)\) n/a 7616 8
7840.2.eq \(\chi_{7840}(717, \cdot)\) n/a 7616 8
7840.2.et \(\chi_{7840}(117, \cdot)\) n/a 7616 8
7840.2.eu \(\chi_{7840}(67, \cdot)\) n/a 7616 8
7840.2.ev \(\chi_{7840}(19, \cdot)\) n/a 7616 8
7840.2.ew \(\chi_{7840}(1341, \cdot)\) n/a 5120 8
7840.2.ez \(\chi_{7840}(377, \cdot)\) None 0 12
7840.2.fb \(\chi_{7840}(183, \cdot)\) None 0 12
7840.2.fd \(\chi_{7840}(463, \cdot)\) n/a 3984 12
7840.2.fg \(\chi_{7840}(993, \cdot)\) n/a 4032 12
7840.2.fj \(\chi_{7840}(279, \cdot)\) None 0 12
7840.2.fk \(\chi_{7840}(281, \cdot)\) None 0 12
7840.2.fl \(\chi_{7840}(951, \cdot)\) None 0 12
7840.2.fm \(\chi_{7840}(169, \cdot)\) None 0 12
7840.2.fp \(\chi_{7840}(433, \cdot)\) n/a 3984 12
7840.2.fs \(\chi_{7840}(127, \cdot)\) n/a 4032 12
7840.2.ft \(\chi_{7840}(407, \cdot)\) None 0 12
7840.2.fv \(\chi_{7840}(153, \cdot)\) None 0 12
7840.2.fx \(\chi_{7840}(159, \cdot)\) n/a 4032 12
7840.2.ga \(\chi_{7840}(81, \cdot)\) n/a 2688 12
7840.2.gc \(\chi_{7840}(271, \cdot)\) n/a 2688 12
7840.2.gd \(\chi_{7840}(289, \cdot)\) n/a 4032 12
7840.2.gg \(\chi_{7840}(529, \cdot)\) n/a 3984 12
7840.2.gh \(\chi_{7840}(831, \cdot)\) n/a 2688 12
7840.2.gl \(\chi_{7840}(719, \cdot)\) n/a 3984 12
7840.2.go \(\chi_{7840}(29, \cdot)\) n/a 32160 24
7840.2.gp \(\chi_{7840}(251, \cdot)\) n/a 21504 24
7840.2.gq \(\chi_{7840}(237, \cdot)\) n/a 32160 24
7840.2.gr \(\chi_{7840}(267, \cdot)\) n/a 32160 24
7840.2.gu \(\chi_{7840}(43, \cdot)\) n/a 32160 24
7840.2.gv \(\chi_{7840}(13, \cdot)\) n/a 32160 24
7840.2.ha \(\chi_{7840}(139, \cdot)\) n/a 32160 24
7840.2.hb \(\chi_{7840}(141, \cdot)\) n/a 21504 24
7840.2.hd \(\chi_{7840}(247, \cdot)\) None 0 24
7840.2.hf \(\chi_{7840}(297, \cdot)\) None 0 24
7840.2.hh \(\chi_{7840}(543, \cdot)\) n/a 8064 24
7840.2.hi \(\chi_{7840}(17, \cdot)\) n/a 7968 24
7840.2.hm \(\chi_{7840}(9, \cdot)\) None 0 24
7840.2.hn \(\chi_{7840}(311, \cdot)\) None 0 24
7840.2.ho \(\chi_{7840}(121, \cdot)\) None 0 24
7840.2.hp \(\chi_{7840}(199, \cdot)\) None 0 24
7840.2.ht \(\chi_{7840}(33, \cdot)\) n/a 8064 24
7840.2.hu \(\chi_{7840}(207, \cdot)\) n/a 7968 24
7840.2.hx \(\chi_{7840}(73, \cdot)\) None 0 24
7840.2.hz \(\chi_{7840}(23, \cdot)\) None 0 24
7840.2.ia \(\chi_{7840}(221, \cdot)\) n/a 43008 48
7840.2.ib \(\chi_{7840}(59, \cdot)\) n/a 64320 48
7840.2.ig \(\chi_{7840}(123, \cdot)\) n/a 64320 48
7840.2.ih \(\chi_{7840}(173, \cdot)\) n/a 64320 48
7840.2.ik \(\chi_{7840}(157, \cdot)\) n/a 64320 48
7840.2.il \(\chi_{7840}(107, \cdot)\) n/a 64320 48
7840.2.im \(\chi_{7840}(131, \cdot)\) n/a 43008 48
7840.2.in \(\chi_{7840}(109, \cdot)\) n/a 64320 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7840)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3920))\)\(^{\oplus 2}\)