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Properties

Label 9438.2
Level 9438
Weight 2
Dimension 592664
Nonzero newspaces 48
Sturm bound 9757440

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Defining parameters

Level: \( N \) = \( 9438 = 2 \cdot 3 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(9757440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9438))\).

Total New Old
Modular forms 2454720 592664 1862056
Cusp forms 2424001 592664 1831337
Eisenstein series 30719 0 30719

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9438))\)

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
9438.2.a \(\chi_{9438}(1, \cdot)\) 9438.2.a.a 1 1
9438.2.a.b 1
9438.2.a.c 1
9438.2.a.d 1
9438.2.a.e 1
9438.2.a.f 1
9438.2.a.g 1
9438.2.a.h 1
9438.2.a.i 1
9438.2.a.j 1
9438.2.a.k 1
9438.2.a.l 1
9438.2.a.m 1
9438.2.a.n 1
9438.2.a.o 1
9438.2.a.p 1
9438.2.a.q 1
9438.2.a.r 1
9438.2.a.s 1
9438.2.a.t 1
9438.2.a.u 1
9438.2.a.v 1
9438.2.a.w 1
9438.2.a.x 1
9438.2.a.y 1
9438.2.a.z 1
9438.2.a.ba 1
9438.2.a.bb 1
9438.2.a.bc 1
9438.2.a.bd 1
9438.2.a.be 2
9438.2.a.bf 2
9438.2.a.bg 2
9438.2.a.bh 2
9438.2.a.bi 2
9438.2.a.bj 2
9438.2.a.bk 2
9438.2.a.bl 2
9438.2.a.bm 2
9438.2.a.bn 2
9438.2.a.bo 2
9438.2.a.bp 2
9438.2.a.bq 2
9438.2.a.br 2
9438.2.a.bs 2
9438.2.a.bt 2
9438.2.a.bu 2
9438.2.a.bv 2
9438.2.a.bw 2
9438.2.a.bx 2
9438.2.a.by 2
9438.2.a.bz 2
9438.2.a.ca 2
9438.2.a.cb 2
9438.2.a.cc 2
9438.2.a.cd 2
9438.2.a.ce 2
9438.2.a.cf 2
9438.2.a.cg 2
9438.2.a.ch 2
9438.2.a.ci 2
9438.2.a.cj 2
9438.2.a.ck 2
9438.2.a.cl 2
9438.2.a.cm 3
9438.2.a.cn 3
9438.2.a.co 3
9438.2.a.cp 3
9438.2.a.cq 4
9438.2.a.cr 4
9438.2.a.cs 4
9438.2.a.ct 4
9438.2.a.cu 4
9438.2.a.cv 4
9438.2.a.cw 4
9438.2.a.cx 4
9438.2.a.cy 6
9438.2.a.cz 6
9438.2.a.da 6
9438.2.a.db 6
9438.2.a.dc 6
9438.2.a.dd 6
9438.2.a.de 6
9438.2.a.df 6
9438.2.a.dg 6
9438.2.a.dh 6
9438.2.a.di 8
9438.2.a.dj 8
9438.2.b \(\chi_{9438}(8711, \cdot)\) n/a 432 1
9438.2.c \(\chi_{9438}(727, \cdot)\) n/a 254 1
9438.2.h \(\chi_{9438}(9437, \cdot)\) n/a 504 1
9438.2.i \(\chi_{9438}(6535, \cdot)\) n/a 508 2
9438.2.l \(\chi_{9438}(967, \cdot)\) n/a 504 2
9438.2.m \(\chi_{9438}(4841, \cdot)\) n/a 1020 2
9438.2.n \(\chi_{9438}(6319, \cdot)\) n/a 864 4
9438.2.q \(\chi_{9438}(1453, \cdot)\) n/a 512 2
9438.2.r \(\chi_{9438}(5807, \cdot)\) n/a 1008 2
9438.2.s \(\chi_{9438}(725, \cdot)\) n/a 1008 2
9438.2.v \(\chi_{9438}(233, \cdot)\) n/a 2016 4
9438.2.ba \(\chi_{9438}(1613, \cdot)\) n/a 1728 4
9438.2.bb \(\chi_{9438}(493, \cdot)\) n/a 1008 4
9438.2.bc \(\chi_{9438}(859, \cdot)\) n/a 2640 10
9438.2.bd \(\chi_{9438}(1211, \cdot)\) n/a 2032 4
9438.2.be \(\chi_{9438}(241, \cdot)\) n/a 1008 4
9438.2.bh \(\chi_{9438}(3415, \cdot)\) n/a 2016 8
9438.2.bi \(\chi_{9438}(1201, \cdot)\) n/a 2016 8
9438.2.bj \(\chi_{9438}(1721, \cdot)\) n/a 4032 8
9438.2.bm \(\chi_{9438}(857, \cdot)\) n/a 6160 10
9438.2.br \(\chi_{9438}(1585, \cdot)\) n/a 3080 10
9438.2.bs \(\chi_{9438}(131, \cdot)\) n/a 5280 10
9438.2.bv \(\chi_{9438}(959, \cdot)\) n/a 4032 8
9438.2.bw \(\chi_{9438}(511, \cdot)\) n/a 2016 8
9438.2.bx \(\chi_{9438}(887, \cdot)\) n/a 4032 8
9438.2.ca \(\chi_{9438}(133, \cdot)\) n/a 6160 20
9438.2.cb \(\chi_{9438}(551, \cdot)\) n/a 12320 20
9438.2.cc \(\chi_{9438}(109, \cdot)\) n/a 6160 20
9438.2.cf \(\chi_{9438}(157, \cdot)\) n/a 10560 40
9438.2.ci \(\chi_{9438}(245, \cdot)\) n/a 8064 16
9438.2.cj \(\chi_{9438}(457, \cdot)\) n/a 4032 16
9438.2.cm \(\chi_{9438}(329, \cdot)\) n/a 12320 20
9438.2.cn \(\chi_{9438}(263, \cdot)\) n/a 12320 20
9438.2.co \(\chi_{9438}(199, \cdot)\) n/a 6160 20
9438.2.cr \(\chi_{9438}(25, \cdot)\) n/a 12320 40
9438.2.cs \(\chi_{9438}(365, \cdot)\) n/a 21120 40
9438.2.cx \(\chi_{9438}(545, \cdot)\) n/a 24640 40
9438.2.da \(\chi_{9438}(175, \cdot)\) n/a 12320 40
9438.2.db \(\chi_{9438}(89, \cdot)\) n/a 24640 40
9438.2.dc \(\chi_{9438}(289, \cdot)\) n/a 24640 80
9438.2.df \(\chi_{9438}(5, \cdot)\) n/a 49280 80
9438.2.dg \(\chi_{9438}(73, \cdot)\) n/a 24640 80
9438.2.dj \(\chi_{9438}(29, \cdot)\) n/a 49280 80
9438.2.dk \(\chi_{9438}(49, \cdot)\) n/a 24640 80
9438.2.dl \(\chi_{9438}(17, \cdot)\) n/a 49280 80
9438.2.do \(\chi_{9438}(7, \cdot)\) n/a 49280 160
9438.2.dp \(\chi_{9438}(59, \cdot)\) n/a 98560 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9438))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9438)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1573))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3146))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4719))\)\(^{\oplus 2}\)