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Properties

Label 7938.2
Level 7938
Weight 2
Dimension 433344
Nonzero newspaces 44
Sturm bound 6858432

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Defining parameters

Level: \( N \) = \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 44 \)
Sturm bound: \(6858432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7938))\).

Total New Old
Modular forms 1727568 433344 1294224
Cusp forms 1701649 433344 1268305
Eisenstein series 25919 0 25919

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7938))\)

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
7938.2.a \(\chi_{7938}(1, \cdot)\) 7938.2.a.a 1 1
7938.2.a.b 1
7938.2.a.c 1
7938.2.a.d 1
7938.2.a.e 1
7938.2.a.f 1
7938.2.a.g 1
7938.2.a.h 1
7938.2.a.i 1
7938.2.a.j 1
7938.2.a.k 1
7938.2.a.l 1
7938.2.a.m 1
7938.2.a.n 1
7938.2.a.o 1
7938.2.a.p 1
7938.2.a.q 1
7938.2.a.r 1
7938.2.a.s 1
7938.2.a.t 1
7938.2.a.u 1
7938.2.a.v 1
7938.2.a.w 1
7938.2.a.x 1
7938.2.a.y 1
7938.2.a.z 1
7938.2.a.ba 1
7938.2.a.bb 1
7938.2.a.bc 1
7938.2.a.bd 1
7938.2.a.be 1
7938.2.a.bf 1
7938.2.a.bg 2
7938.2.a.bh 2
7938.2.a.bi 2
7938.2.a.bj 2
7938.2.a.bk 2
7938.2.a.bl 2
7938.2.a.bm 2
7938.2.a.bn 2
7938.2.a.bo 2
7938.2.a.bp 2
7938.2.a.bq 2
7938.2.a.br 2
7938.2.a.bs 2
7938.2.a.bt 2
7938.2.a.bu 3
7938.2.a.bv 3
7938.2.a.bw 3
7938.2.a.bx 3
7938.2.a.by 3
7938.2.a.bz 3
7938.2.a.ca 3
7938.2.a.cb 3
7938.2.a.cc 4
7938.2.a.cd 4
7938.2.a.ce 4
7938.2.a.cf 4
7938.2.a.cg 4
7938.2.a.ch 4
7938.2.a.ci 4
7938.2.a.cj 4
7938.2.a.ck 4
7938.2.a.cl 4
7938.2.a.cm 4
7938.2.a.cn 4
7938.2.a.co 4
7938.2.a.cp 4
7938.2.a.cq 4
7938.2.a.cr 4
7938.2.a.cs 4
7938.2.a.ct 4
7938.2.a.cu 4
7938.2.a.cv 4
7938.2.d \(\chi_{7938}(7937, \cdot)\) n/a 160 1
7938.2.e \(\chi_{7938}(6535, \cdot)\) n/a 320 2
7938.2.f \(\chi_{7938}(2647, \cdot)\) n/a 328 2
7938.2.g \(\chi_{7938}(2431, \cdot)\) n/a 320 2
7938.2.h \(\chi_{7938}(1243, \cdot)\) n/a 320 2
7938.2.k \(\chi_{7938}(4049, \cdot)\) n/a 320 2
7938.2.l \(\chi_{7938}(215, \cdot)\) n/a 320 2
7938.2.m \(\chi_{7938}(2645, \cdot)\) n/a 320 2
7938.2.t \(\chi_{7938}(2861, \cdot)\) n/a 320 2
7938.2.u \(\chi_{7938}(1135, \cdot)\) n/a 1344 6
7938.2.v \(\chi_{7938}(883, \cdot)\) n/a 738 6
7938.2.w \(\chi_{7938}(361, \cdot)\) n/a 720 6
7938.2.x \(\chi_{7938}(1549, \cdot)\) n/a 720 6
7938.2.y \(\chi_{7938}(1133, \cdot)\) n/a 1344 6
7938.2.bd \(\chi_{7938}(881, \cdot)\) n/a 720 6
7938.2.be \(\chi_{7938}(1979, \cdot)\) n/a 720 6
7938.2.bj \(\chi_{7938}(521, \cdot)\) n/a 720 6
7938.2.bk \(\chi_{7938}(109, \cdot)\) n/a 2688 12
7938.2.bl \(\chi_{7938}(163, \cdot)\) n/a 2688 12
7938.2.bm \(\chi_{7938}(379, \cdot)\) n/a 2688 12
7938.2.bn \(\chi_{7938}(865, \cdot)\) n/a 2688 12
7938.2.bo \(\chi_{7938}(67, \cdot)\) n/a 6480 18
7938.2.bp \(\chi_{7938}(295, \cdot)\) n/a 6642 18
7938.2.bq \(\chi_{7938}(373, \cdot)\) n/a 6480 18
7938.2.br \(\chi_{7938}(593, \cdot)\) n/a 2688 12
7938.2.by \(\chi_{7938}(377, \cdot)\) n/a 2688 12
7938.2.bz \(\chi_{7938}(269, \cdot)\) n/a 2688 12
7938.2.ca \(\chi_{7938}(647, \cdot)\) n/a 2688 12
7938.2.ce \(\chi_{7938}(227, \cdot)\) n/a 6480 18
7938.2.cj \(\chi_{7938}(803, \cdot)\) n/a 6480 18
7938.2.ck \(\chi_{7938}(293, \cdot)\) n/a 6480 18
7938.2.cm \(\chi_{7938}(37, \cdot)\) n/a 6048 36
7938.2.cn \(\chi_{7938}(289, \cdot)\) n/a 6048 36
7938.2.co \(\chi_{7938}(127, \cdot)\) n/a 6048 36
7938.2.cp \(\chi_{7938}(143, \cdot)\) n/a 6048 36
7938.2.cu \(\chi_{7938}(17, \cdot)\) n/a 6048 36
7938.2.cv \(\chi_{7938}(125, \cdot)\) n/a 6048 36
7938.2.cy \(\chi_{7938}(25, \cdot)\) n/a 54432 108
7938.2.cz \(\chi_{7938}(43, \cdot)\) n/a 54432 108
7938.2.da \(\chi_{7938}(193, \cdot)\) n/a 54432 108
7938.2.dc \(\chi_{7938}(41, \cdot)\) n/a 54432 108
7938.2.dd \(\chi_{7938}(47, \cdot)\) n/a 54432 108
7938.2.di \(\chi_{7938}(5, \cdot)\) n/a 54432 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7938))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7938)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1323))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2646))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3969))\)\(^{\oplus 2}\)