Properties

Label 9408.2
Level 9408
Weight 2
Dimension 972890
Nonzero newspaces 64
Sturm bound 9633792

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Defining parameters

Level: \( N \) = \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(9633792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9408))\).

Total New Old
Modular forms 2425728 977158 1448570
Cusp forms 2391169 972890 1418279
Eisenstein series 34559 4268 30291

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9408))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9408.2.a \(\chi_{9408}(1, \cdot)\) 9408.2.a.a 1 1
9408.2.a.b 1
9408.2.a.c 1
9408.2.a.d 1
9408.2.a.e 1
9408.2.a.f 1
9408.2.a.g 1
9408.2.a.h 1
9408.2.a.i 1
9408.2.a.j 1
9408.2.a.k 1
9408.2.a.l 1
9408.2.a.m 1
9408.2.a.n 1
9408.2.a.o 1
9408.2.a.p 1
9408.2.a.q 1
9408.2.a.r 1
9408.2.a.s 1
9408.2.a.t 1
9408.2.a.u 1
9408.2.a.v 1
9408.2.a.w 1
9408.2.a.x 1
9408.2.a.y 1
9408.2.a.z 1
9408.2.a.ba 1
9408.2.a.bb 1
9408.2.a.bc 1
9408.2.a.bd 1
9408.2.a.be 1
9408.2.a.bf 1
9408.2.a.bg 1
9408.2.a.bh 1
9408.2.a.bi 1
9408.2.a.bj 1
9408.2.a.bk 1
9408.2.a.bl 1
9408.2.a.bm 1
9408.2.a.bn 1
9408.2.a.bo 1
9408.2.a.bp 1
9408.2.a.bq 1
9408.2.a.br 1
9408.2.a.bs 1
9408.2.a.bt 1
9408.2.a.bu 1
9408.2.a.bv 1
9408.2.a.bw 1
9408.2.a.bx 1
9408.2.a.by 1
9408.2.a.bz 1
9408.2.a.ca 1
9408.2.a.cb 1
9408.2.a.cc 1
9408.2.a.cd 1
9408.2.a.ce 1
9408.2.a.cf 1
9408.2.a.cg 1
9408.2.a.ch 1
9408.2.a.ci 1
9408.2.a.cj 1
9408.2.a.ck 1
9408.2.a.cl 1
9408.2.a.cm 1
9408.2.a.cn 1
9408.2.a.co 1
9408.2.a.cp 1
9408.2.a.cq 1
9408.2.a.cr 1
9408.2.a.cs 1
9408.2.a.ct 1
9408.2.a.cu 1
9408.2.a.cv 1
9408.2.a.cw 1
9408.2.a.cx 1
9408.2.a.cy 1
9408.2.a.cz 1
9408.2.a.da 1
9408.2.a.db 1
9408.2.a.dc 1
9408.2.a.dd 1
9408.2.a.de 1
9408.2.a.df 1
9408.2.a.dg 2
9408.2.a.dh 2
9408.2.a.di 2
9408.2.a.dj 2
9408.2.a.dk 2
9408.2.a.dl 2
9408.2.a.dm 2
9408.2.a.dn 2
9408.2.a.do 2
9408.2.a.dp 2
9408.2.a.dq 2
9408.2.a.dr 2
9408.2.a.ds 2
9408.2.a.dt 2
9408.2.a.du 2
9408.2.a.dv 2
9408.2.a.dw 2
9408.2.a.dx 2
9408.2.a.dy 2
9408.2.a.dz 2
9408.2.a.ea 2
9408.2.a.eb 2
9408.2.a.ec 2
9408.2.a.ed 2
9408.2.a.ee 2
9408.2.a.ef 2
9408.2.a.eg 3
9408.2.a.eh 3
9408.2.a.ei 3
9408.2.a.ej 3
9408.2.a.ek 4
9408.2.a.el 4
9408.2.a.em 4
9408.2.a.en 4
9408.2.b \(\chi_{9408}(6271, \cdot)\) n/a 160 1
9408.2.c \(\chi_{9408}(4705, \cdot)\) n/a 164 1
9408.2.h \(\chi_{9408}(4607, \cdot)\) n/a 318 1
9408.2.i \(\chi_{9408}(3233, \cdot)\) n/a 320 1
9408.2.j \(\chi_{9408}(9311, \cdot)\) n/a 328 1
9408.2.k \(\chi_{9408}(7937, \cdot)\) n/a 312 1
9408.2.p \(\chi_{9408}(1567, \cdot)\) n/a 160 1
9408.2.q \(\chi_{9408}(961, \cdot)\) n/a 320 2
9408.2.s \(\chi_{9408}(2255, \cdot)\) n/a 636 2
9408.2.u \(\chi_{9408}(3919, \cdot)\) n/a 320 2
9408.2.w \(\chi_{9408}(2353, \cdot)\) n/a 328 2
9408.2.y \(\chi_{9408}(881, \cdot)\) n/a 624 2
9408.2.bb \(\chi_{9408}(31, \cdot)\) n/a 320 2
9408.2.bc \(\chi_{9408}(6401, \cdot)\) n/a 624 2
9408.2.bd \(\chi_{9408}(863, \cdot)\) n/a 640 2
9408.2.bi \(\chi_{9408}(1697, \cdot)\) n/a 640 2
9408.2.bj \(\chi_{9408}(5567, \cdot)\) n/a 624 2
9408.2.bk \(\chi_{9408}(5665, \cdot)\) n/a 320 2
9408.2.bl \(\chi_{9408}(4735, \cdot)\) n/a 320 2
9408.2.bo \(\chi_{9408}(1345, \cdot)\) n/a 1344 6
9408.2.bp \(\chi_{9408}(2057, \cdot)\) None 0 4
9408.2.br \(\chi_{9408}(1177, \cdot)\) None 0 4
9408.2.bt \(\chi_{9408}(1079, \cdot)\) None 0 4
9408.2.bv \(\chi_{9408}(391, \cdot)\) None 0 4
9408.2.bx \(\chi_{9408}(4049, \cdot)\) n/a 1248 4
9408.2.bz \(\chi_{9408}(3313, \cdot)\) n/a 640 4
9408.2.cb \(\chi_{9408}(2383, \cdot)\) n/a 640 4
9408.2.cd \(\chi_{9408}(3215, \cdot)\) n/a 1248 4
9408.2.cf \(\chi_{9408}(223, \cdot)\) n/a 1344 6
9408.2.ck \(\chi_{9408}(1217, \cdot)\) n/a 2664 6
9408.2.cl \(\chi_{9408}(1247, \cdot)\) n/a 2688 6
9408.2.cm \(\chi_{9408}(545, \cdot)\) n/a 2688 6
9408.2.cn \(\chi_{9408}(575, \cdot)\) n/a 2664 6
9408.2.cs \(\chi_{9408}(673, \cdot)\) n/a 1344 6
9408.2.ct \(\chi_{9408}(895, \cdot)\) n/a 1344 6
9408.2.cw \(\chi_{9408}(589, \cdot)\) n/a 5248 8
9408.2.cx \(\chi_{9408}(979, \cdot)\) n/a 5120 8
9408.2.cy \(\chi_{9408}(491, \cdot)\) n/a 10416 8
9408.2.cz \(\chi_{9408}(293, \cdot)\) n/a 10176 8
9408.2.dc \(\chi_{9408}(193, \cdot)\) n/a 2688 12
9408.2.de \(\chi_{9408}(1207, \cdot)\) None 0 8
9408.2.dg \(\chi_{9408}(263, \cdot)\) None 0 8
9408.2.di \(\chi_{9408}(361, \cdot)\) None 0 8
9408.2.dk \(\chi_{9408}(521, \cdot)\) None 0 8
9408.2.dl \(\chi_{9408}(209, \cdot)\) n/a 5328 12
9408.2.dn \(\chi_{9408}(337, \cdot)\) n/a 2688 12
9408.2.dp \(\chi_{9408}(559, \cdot)\) n/a 2688 12
9408.2.dr \(\chi_{9408}(239, \cdot)\) n/a 5328 12
9408.2.dv \(\chi_{9408}(703, \cdot)\) n/a 2688 12
9408.2.dw \(\chi_{9408}(289, \cdot)\) n/a 2688 12
9408.2.dx \(\chi_{9408}(191, \cdot)\) n/a 5328 12
9408.2.dy \(\chi_{9408}(353, \cdot)\) n/a 5376 12
9408.2.ed \(\chi_{9408}(95, \cdot)\) n/a 5376 12
9408.2.ee \(\chi_{9408}(257, \cdot)\) n/a 5328 12
9408.2.ef \(\chi_{9408}(1375, \cdot)\) n/a 2688 12
9408.2.ek \(\chi_{9408}(509, \cdot)\) n/a 20352 16
9408.2.el \(\chi_{9408}(275, \cdot)\) n/a 20352 16
9408.2.em \(\chi_{9408}(19, \cdot)\) n/a 10240 16
9408.2.en \(\chi_{9408}(373, \cdot)\) n/a 10240 16
9408.2.er \(\chi_{9408}(71, \cdot)\) None 0 24
9408.2.et \(\chi_{9408}(55, \cdot)\) None 0 24
9408.2.ev \(\chi_{9408}(41, \cdot)\) None 0 24
9408.2.ex \(\chi_{9408}(169, \cdot)\) None 0 24
9408.2.ez \(\chi_{9408}(431, \cdot)\) n/a 10656 24
9408.2.fb \(\chi_{9408}(271, \cdot)\) n/a 5376 24
9408.2.fd \(\chi_{9408}(529, \cdot)\) n/a 5376 24
9408.2.ff \(\chi_{9408}(17, \cdot)\) n/a 10656 24
9408.2.fg \(\chi_{9408}(139, \cdot)\) n/a 43008 48
9408.2.fh \(\chi_{9408}(85, \cdot)\) n/a 43008 48
9408.2.fm \(\chi_{9408}(125, \cdot)\) n/a 85824 48
9408.2.fn \(\chi_{9408}(155, \cdot)\) n/a 85824 48
9408.2.fo \(\chi_{9408}(25, \cdot)\) None 0 48
9408.2.fq \(\chi_{9408}(89, \cdot)\) None 0 48
9408.2.fs \(\chi_{9408}(103, \cdot)\) None 0 48
9408.2.fu \(\chi_{9408}(23, \cdot)\) None 0 48
9408.2.fw \(\chi_{9408}(11, \cdot)\) n/a 171648 96
9408.2.fx \(\chi_{9408}(5, \cdot)\) n/a 171648 96
9408.2.gc \(\chi_{9408}(37, \cdot)\) n/a 86016 96
9408.2.gd \(\chi_{9408}(115, \cdot)\) n/a 86016 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9408))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9408)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1344))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4704))\)\(^{\oplus 2}\)