# Properties

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(9408)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 42}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 21}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(672))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1176))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1344))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1568))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2352))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3136))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4704))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9408))$$$$^{\oplus 1}$$