Properties

Label 10404.2
Level 10404
Weight 2
Dimension 1370857
Nonzero newspaces 40
Sturm bound 11985408

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 10404 = 2^{2} \cdot 3^{2} \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(11985408\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(10404))\).

Total New Old
Modular forms 3012352 1377489 1634863
Cusp forms 2980353 1370857 1609496
Eisenstein series 31999 6632 25367

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(10404))\)

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
10404.2.a \(\chi_{10404}(1, \cdot)\) 10404.2.a.a 1 1
10404.2.a.b 1
10404.2.a.c 1
10404.2.a.d 1
10404.2.a.e 1
10404.2.a.f 1
10404.2.a.g 1
10404.2.a.h 1
10404.2.a.i 1
10404.2.a.j 1
10404.2.a.k 1
10404.2.a.l 1
10404.2.a.m 1
10404.2.a.n 1
10404.2.a.o 1
10404.2.a.p 2
10404.2.a.q 2
10404.2.a.r 2
10404.2.a.s 2
10404.2.a.t 2
10404.2.a.u 2
10404.2.a.v 2
10404.2.a.w 2
10404.2.a.x 2
10404.2.a.y 2
10404.2.a.z 3
10404.2.a.ba 3
10404.2.a.bb 3
10404.2.a.bc 3
10404.2.a.bd 3
10404.2.a.be 3
10404.2.a.bf 4
10404.2.a.bg 4
10404.2.a.bh 4
10404.2.a.bi 6
10404.2.a.bj 6
10404.2.a.bk 6
10404.2.a.bl 6
10404.2.a.bm 8
10404.2.a.bn 8
10404.2.a.bo 8
10404.2.b \(\chi_{10404}(577, \cdot)\) n/a 112 1
10404.2.c \(\chi_{10404}(9827, \cdot)\) n/a 542 1
10404.2.h \(\chi_{10404}(10403, \cdot)\) n/a 540 1
10404.2.i \(\chi_{10404}(3469, \cdot)\) n/a 542 2
10404.2.k \(\chi_{10404}(829, \cdot)\) n/a 224 2
10404.2.m \(\chi_{10404}(251, \cdot)\) n/a 1080 2
10404.2.n \(\chi_{10404}(3467, \cdot)\) n/a 3184 2
10404.2.s \(\chi_{10404}(2891, \cdot)\) n/a 3192 2
10404.2.t \(\chi_{10404}(4045, \cdot)\) n/a 540 2
10404.2.w \(\chi_{10404}(757, \cdot)\) n/a 452 4
10404.2.x \(\chi_{10404}(179, \cdot)\) n/a 2160 4
10404.2.z \(\chi_{10404}(3217, \cdot)\) n/a 1080 4
10404.2.bb \(\chi_{10404}(2639, \cdot)\) n/a 6368 4
10404.2.bc \(\chi_{10404}(1025, \cdot)\) n/a 720 8
10404.2.bd \(\chi_{10404}(1603, \cdot)\) n/a 5288 8
10404.2.bg \(\chi_{10404}(613, \cdot)\) n/a 2048 16
10404.2.bj \(\chi_{10404}(733, \cdot)\) n/a 2160 8
10404.2.bk \(\chi_{10404}(155, \cdot)\) n/a 12736 8
10404.2.bl \(\chi_{10404}(611, \cdot)\) n/a 9792 16
10404.2.bq \(\chi_{10404}(35, \cdot)\) n/a 9792 16
10404.2.br \(\chi_{10404}(1189, \cdot)\) n/a 2048 16
10404.2.bs \(\chi_{10404}(643, \cdot)\) n/a 25472 16
10404.2.bt \(\chi_{10404}(65, \cdot)\) n/a 4320 16
10404.2.bw \(\chi_{10404}(205, \cdot)\) n/a 9792 32
10404.2.bx \(\chi_{10404}(395, \cdot)\) n/a 19584 32
10404.2.bz \(\chi_{10404}(217, \cdot)\) n/a 4096 32
10404.2.cb \(\chi_{10404}(169, \cdot)\) n/a 9792 32
10404.2.cc \(\chi_{10404}(239, \cdot)\) n/a 58624 32
10404.2.ch \(\chi_{10404}(203, \cdot)\) n/a 58624 32
10404.2.ci \(\chi_{10404}(287, \cdot)\) n/a 39168 64
10404.2.cj \(\chi_{10404}(145, \cdot)\) n/a 8128 64
10404.2.cm \(\chi_{10404}(47, \cdot)\) n/a 117248 64
10404.2.co \(\chi_{10404}(13, \cdot)\) n/a 19584 64
10404.2.cs \(\chi_{10404}(91, \cdot)\) n/a 97664 128
10404.2.ct \(\chi_{10404}(125, \cdot)\) n/a 13056 128
10404.2.cu \(\chi_{10404}(59, \cdot)\) n/a 234496 128
10404.2.cv \(\chi_{10404}(25, \cdot)\) n/a 39168 128
10404.2.da \(\chi_{10404}(5, \cdot)\) n/a 78336 256
10404.2.db \(\chi_{10404}(7, \cdot)\) n/a 468992 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(10404))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(10404)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2601))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3468))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5202))\)\(^{\oplus 2}\)