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Properties

Label 10304.2
Level 10304
Weight 2
Dimension 1737492
Nonzero newspaces 64
Sturm bound 12976128

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Defining parameters

Level: \( N \) = \( 10304 = 2^{6} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(12976128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(10304))\).

Total New Old
Modular forms 3263040 1746732 1516308
Cusp forms 3225025 1737492 1487533
Eisenstein series 38015 9240 28775

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(10304))\)

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
10304.2.a \(\chi_{10304}(1, \cdot)\) 10304.2.a.a 1 1
10304.2.a.b 1
10304.2.a.c 1
10304.2.a.d 1
10304.2.a.e 1
10304.2.a.f 1
10304.2.a.g 1
10304.2.a.h 1
10304.2.a.i 1
10304.2.a.j 1
10304.2.a.k 1
10304.2.a.l 1
10304.2.a.m 1
10304.2.a.n 1
10304.2.a.o 1
10304.2.a.p 1
10304.2.a.q 1
10304.2.a.r 1
10304.2.a.s 1
10304.2.a.t 1
10304.2.a.u 1
10304.2.a.v 1
10304.2.a.w 1
10304.2.a.x 1
10304.2.a.y 1
10304.2.a.z 1
10304.2.a.ba 1
10304.2.a.bb 1
10304.2.a.bc 1
10304.2.a.bd 1
10304.2.a.be 1
10304.2.a.bf 1
10304.2.a.bg 1
10304.2.a.bh 1
10304.2.a.bi 1
10304.2.a.bj 1
10304.2.a.bk 1
10304.2.a.bl 1
10304.2.a.bm 2
10304.2.a.bn 2
10304.2.a.bo 2
10304.2.a.bp 2
10304.2.a.bq 2
10304.2.a.br 2
10304.2.a.bs 2
10304.2.a.bt 2
10304.2.a.bu 2
10304.2.a.bv 2
10304.2.a.bw 2
10304.2.a.bx 2
10304.2.a.by 2
10304.2.a.bz 2
10304.2.a.ca 2
10304.2.a.cb 2
10304.2.a.cc 3
10304.2.a.cd 3
10304.2.a.ce 3
10304.2.a.cf 3
10304.2.a.cg 3
10304.2.a.ch 3
10304.2.a.ci 3
10304.2.a.cj 3
10304.2.a.ck 3
10304.2.a.cl 3
10304.2.a.cm 4
10304.2.a.cn 4
10304.2.a.co 4
10304.2.a.cp 4
10304.2.a.cq 4
10304.2.a.cr 4
10304.2.a.cs 4
10304.2.a.ct 4
10304.2.a.cu 5
10304.2.a.cv 5
10304.2.a.cw 5
10304.2.a.cx 5
10304.2.a.cy 5
10304.2.a.cz 5
10304.2.a.da 5
10304.2.a.db 5
10304.2.a.dc 7
10304.2.a.dd 7
10304.2.a.de 7
10304.2.a.df 7
10304.2.a.dg 9
10304.2.a.dh 9
10304.2.a.di 11
10304.2.a.dj 11
10304.2.a.dk 12
10304.2.a.dl 12
10304.2.b \(\chi_{10304}(5153, \cdot)\) n/a 264 1
10304.2.e \(\chi_{10304}(1471, \cdot)\) n/a 288 1
10304.2.f \(\chi_{10304}(321, \cdot)\) n/a 380 1
10304.2.i \(\chi_{10304}(3359, \cdot)\) n/a 352 1
10304.2.j \(\chi_{10304}(8511, \cdot)\) n/a 352 1
10304.2.m \(\chi_{10304}(5473, \cdot)\) n/a 384 1
10304.2.n \(\chi_{10304}(6623, \cdot)\) n/a 288 1
10304.2.q \(\chi_{10304}(5889, \cdot)\) n/a 704 2
10304.2.s \(\chi_{10304}(783, \cdot)\) n/a 704 2
10304.2.t \(\chi_{10304}(2897, \cdot)\) n/a 760 2
10304.2.w \(\chi_{10304}(4047, \cdot)\) n/a 576 2
10304.2.x \(\chi_{10304}(2577, \cdot)\) n/a 528 2
10304.2.ba \(\chi_{10304}(2207, \cdot)\) n/a 768 2
10304.2.bd \(\chi_{10304}(8417, \cdot)\) n/a 768 2
10304.2.be \(\chi_{10304}(1151, \cdot)\) n/a 704 2
10304.2.bh \(\chi_{10304}(6303, \cdot)\) n/a 704 2
10304.2.bi \(\chi_{10304}(3265, \cdot)\) n/a 760 2
10304.2.bl \(\chi_{10304}(7359, \cdot)\) n/a 760 2
10304.2.bm \(\chi_{10304}(737, \cdot)\) n/a 704 2
10304.2.bw \(\chi_{10304}(449, \cdot)\) n/a 2880 10
10304.2.by \(\chi_{10304}(689, \cdot)\) n/a 1520 4
10304.2.bz \(\chi_{10304}(47, \cdot)\) n/a 1408 4
10304.2.cc \(\chi_{10304}(3313, \cdot)\) n/a 1408 4
10304.2.cd \(\chi_{10304}(1103, \cdot)\) n/a 1520 4
10304.2.cg \(\chi_{10304}(645, \cdot)\) n/a 8448 8
10304.2.ci \(\chi_{10304}(139, \cdot)\) n/a 11264 8
10304.2.cj \(\chi_{10304}(965, \cdot)\) n/a 12256 8
10304.2.cl \(\chi_{10304}(827, \cdot)\) n/a 9216 8
10304.2.cp \(\chi_{10304}(799, \cdot)\) n/a 2880 10
10304.2.cq \(\chi_{10304}(97, \cdot)\) n/a 3840 10
10304.2.ct \(\chi_{10304}(1343, \cdot)\) n/a 3800 10
10304.2.cu \(\chi_{10304}(223, \cdot)\) n/a 3840 10
10304.2.cx \(\chi_{10304}(769, \cdot)\) n/a 3800 10
10304.2.cy \(\chi_{10304}(1023, \cdot)\) n/a 2880 10
10304.2.db \(\chi_{10304}(225, \cdot)\) n/a 2880 10
10304.2.dk \(\chi_{10304}(193, \cdot)\) n/a 7600 20
10304.2.dm \(\chi_{10304}(561, \cdot)\) n/a 5760 20
10304.2.dn \(\chi_{10304}(15, \cdot)\) n/a 5760 20
10304.2.dq \(\chi_{10304}(433, \cdot)\) n/a 7600 20
10304.2.dr \(\chi_{10304}(335, \cdot)\) n/a 7600 20
10304.2.du \(\chi_{10304}(275, \cdot)\) n/a 24512 16
10304.2.dw \(\chi_{10304}(45, \cdot)\) n/a 24512 16
10304.2.dx \(\chi_{10304}(507, \cdot)\) n/a 22528 16
10304.2.dz \(\chi_{10304}(93, \cdot)\) n/a 22528 16
10304.2.ec \(\chi_{10304}(289, \cdot)\) n/a 7680 20
10304.2.ed \(\chi_{10304}(191, \cdot)\) n/a 7600 20
10304.2.eg \(\chi_{10304}(129, \cdot)\) n/a 7600 20
10304.2.eh \(\chi_{10304}(31, \cdot)\) n/a 7680 20
10304.2.ek \(\chi_{10304}(255, \cdot)\) n/a 7600 20
10304.2.el \(\chi_{10304}(33, \cdot)\) n/a 7680 20
10304.2.eo \(\chi_{10304}(543, \cdot)\) n/a 7680 20
10304.2.ez \(\chi_{10304}(79, \cdot)\) n/a 15200 40
10304.2.fa \(\chi_{10304}(81, \cdot)\) n/a 15200 40
10304.2.fd \(\chi_{10304}(271, \cdot)\) n/a 15200 40
10304.2.fe \(\chi_{10304}(17, \cdot)\) n/a 15200 40
10304.2.fh \(\chi_{10304}(43, \cdot)\) n/a 92160 80
10304.2.fj \(\chi_{10304}(125, \cdot)\) n/a 122560 80
10304.2.fk \(\chi_{10304}(27, \cdot)\) n/a 122560 80
10304.2.fm \(\chi_{10304}(29, \cdot)\) n/a 92160 80
10304.2.fx \(\chi_{10304}(165, \cdot)\) n/a 245120 160
10304.2.fz \(\chi_{10304}(3, \cdot)\) n/a 245120 160
10304.2.ga \(\chi_{10304}(5, \cdot)\) n/a 245120 160
10304.2.gc \(\chi_{10304}(11, \cdot)\) n/a 245120 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(10304))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(10304)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5152))\)\(^{\oplus 2}\)