# Properties

 Label 9450.2 Level 9450 Weight 2 Dimension 542676 Nonzero newspaces 96 Sturm bound 9.3312e+06

## Defining parameters

 Level: $$N$$ = $$9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$9331200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9450))$$.

Total New Old
Modular forms 2352960 542676 1810284
Cusp forms 2312641 542676 1769965
Eisenstein series 40319 0 40319

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9450))$$

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
9450.2.a $$\chi_{9450}(1, \cdot)$$ 9450.2.a.a 1 1
9450.2.a.b 1
9450.2.a.c 1
9450.2.a.d 1
9450.2.a.e 1
9450.2.a.f 1
9450.2.a.g 1
9450.2.a.h 1
9450.2.a.i 1
9450.2.a.j 1
9450.2.a.k 1
9450.2.a.l 1
9450.2.a.m 1
9450.2.a.n 1
9450.2.a.o 1
9450.2.a.p 1
9450.2.a.q 1
9450.2.a.r 1
9450.2.a.s 1
9450.2.a.t 1
9450.2.a.u 1
9450.2.a.v 1
9450.2.a.w 1
9450.2.a.x 1
9450.2.a.y 1
9450.2.a.z 1
9450.2.a.ba 1
9450.2.a.bb 1
9450.2.a.bc 1
9450.2.a.bd 1
9450.2.a.be 1
9450.2.a.bf 1
9450.2.a.bg 1
9450.2.a.bh 1
9450.2.a.bi 1
9450.2.a.bj 1
9450.2.a.bk 1
9450.2.a.bl 1
9450.2.a.bm 1
9450.2.a.bn 1
9450.2.a.bo 1
9450.2.a.bp 1
9450.2.a.bq 1
9450.2.a.br 1
9450.2.a.bs 1
9450.2.a.bt 1
9450.2.a.bu 1
9450.2.a.bv 1
9450.2.a.bw 1
9450.2.a.bx 1
9450.2.a.by 1
9450.2.a.bz 1
9450.2.a.ca 1
9450.2.a.cb 1
9450.2.a.cc 1
9450.2.a.cd 1
9450.2.a.ce 1
9450.2.a.cf 1
9450.2.a.cg 1
9450.2.a.ch 1
9450.2.a.ci 1
9450.2.a.cj 1
9450.2.a.ck 1
9450.2.a.cl 1
9450.2.a.cm 1
9450.2.a.cn 1
9450.2.a.co 1
9450.2.a.cp 1
9450.2.a.cq 1
9450.2.a.cr 1
9450.2.a.cs 1
9450.2.a.ct 1
9450.2.a.cu 1
9450.2.a.cv 1
9450.2.a.cw 1
9450.2.a.cx 1
9450.2.a.cy 1
9450.2.a.cz 1
9450.2.a.da 1
9450.2.a.db 1
9450.2.a.dc 1
9450.2.a.dd 1
9450.2.a.de 1
9450.2.a.df 1
9450.2.a.dg 1
9450.2.a.dh 1
9450.2.a.di 1
9450.2.a.dj 1
9450.2.a.dk 1
9450.2.a.dl 1
9450.2.a.dm 1
9450.2.a.dn 1
9450.2.a.do 1
9450.2.a.dp 1
9450.2.a.dq 1
9450.2.a.dr 1
9450.2.a.ds 1
9450.2.a.dt 1
9450.2.a.du 1
9450.2.a.dv 1
9450.2.a.dw 1
9450.2.a.dx 1
9450.2.a.dy 1
9450.2.a.dz 1
9450.2.a.ea 2
9450.2.a.eb 2
9450.2.a.ec 2
9450.2.a.ed 2
9450.2.a.ee 2
9450.2.a.ef 2
9450.2.a.eg 2
9450.2.a.eh 2
9450.2.a.ei 2
9450.2.a.ej 2
9450.2.a.ek 2
9450.2.a.el 2
9450.2.a.em 2
9450.2.a.en 2
9450.2.a.eo 2
9450.2.a.ep 2
9450.2.a.eq 2
9450.2.a.er 2
9450.2.a.es 2
9450.2.a.et 2
9450.2.a.eu 2
9450.2.a.ev 2
9450.2.a.ew 2
9450.2.a.ex 2
9450.2.b $$\chi_{9450}(3401, \cdot)$$ n/a 204 1
9450.2.d $$\chi_{9450}(9449, \cdot)$$ n/a 192 1
9450.2.g $$\chi_{9450}(6049, \cdot)$$ n/a 144 1
9450.2.i $$\chi_{9450}(4951, \cdot)$$ n/a 304 2
9450.2.j $$\chi_{9450}(3151, \cdot)$$ n/a 228 2
9450.2.k $$\chi_{9450}(5401, \cdot)$$ n/a 404 2
9450.2.l $$\chi_{9450}(1801, \cdot)$$ n/a 304 2
9450.2.m $$\chi_{9450}(1457, \cdot)$$ n/a 288 2
9450.2.p $$\chi_{9450}(3457, \cdot)$$ n/a 384 2
9450.2.q $$\chi_{9450}(1891, \cdot)$$ n/a 960 4
9450.2.s $$\chi_{9450}(7199, \cdot)$$ n/a 288 2
9450.2.u $$\chi_{9450}(1151, \cdot)$$ n/a 304 2
9450.2.v $$\chi_{9450}(1999, \cdot)$$ n/a 384 2
9450.2.ba $$\chi_{9450}(2899, \cdot)$$ n/a 216 2
9450.2.bb $$\chi_{9450}(1549, \cdot)$$ n/a 288 2
9450.2.bf $$\chi_{9450}(4751, \cdot)$$ n/a 404 2
9450.2.bg $$\chi_{9450}(3149, \cdot)$$ n/a 288 2
9450.2.bj $$\chi_{9450}(899, \cdot)$$ n/a 288 2
9450.2.bl $$\chi_{9450}(4301, \cdot)$$ n/a 304 2
9450.2.bm $$\chi_{9450}(251, \cdot)$$ n/a 304 2
9450.2.bp $$\chi_{9450}(1349, \cdot)$$ n/a 384 2
9450.2.br $$\chi_{9450}(7849, \cdot)$$ n/a 288 2
9450.2.bt $$\chi_{9450}(1051, \cdot)$$ n/a 2052 6
9450.2.bu $$\chi_{9450}(1201, \cdot)$$ n/a 2736 6
9450.2.bv $$\chi_{9450}(151, \cdot)$$ n/a 2736 6
9450.2.bx $$\chi_{9450}(379, \cdot)$$ n/a 960 4
9450.2.ca $$\chi_{9450}(1889, \cdot)$$ n/a 1280 4
9450.2.cc $$\chi_{9450}(1511, \cdot)$$ n/a 1280 4
9450.2.ce $$\chi_{9450}(557, \cdot)$$ n/a 576 4
9450.2.cg $$\chi_{9450}(2593, \cdot)$$ n/a 768 4
9450.2.ch $$\chi_{9450}(1207, \cdot)$$ n/a 576 4
9450.2.ck $$\chi_{9450}(307, \cdot)$$ n/a 576 4
9450.2.cl $$\chi_{9450}(2843, \cdot)$$ n/a 432 4
9450.2.co $$\chi_{9450}(3257, \cdot)$$ n/a 576 4
9450.2.cp $$\chi_{9450}(107, \cdot)$$ n/a 768 4
9450.2.cr $$\chi_{9450}(3043, \cdot)$$ n/a 576 4
9450.2.ct $$\chi_{9450}(361, \cdot)$$ n/a 1920 8
9450.2.cu $$\chi_{9450}(541, \cdot)$$ n/a 2560 8
9450.2.cv $$\chi_{9450}(631, \cdot)$$ n/a 1440 8
9450.2.cw $$\chi_{9450}(991, \cdot)$$ n/a 1920 8
9450.2.cy $$\chi_{9450}(2399, \cdot)$$ n/a 2592 6
9450.2.da $$\chi_{9450}(499, \cdot)$$ n/a 2592 6
9450.2.de $$\chi_{9450}(1301, \cdot)$$ n/a 2736 6
9450.2.dg $$\chi_{9450}(551, \cdot)$$ n/a 2736 6
9450.2.dh $$\chi_{9450}(949, \cdot)$$ n/a 2592 6
9450.2.dj $$\chi_{9450}(799, \cdot)$$ n/a 1944 6
9450.2.dl $$\chi_{9450}(299, \cdot)$$ n/a 2592 6
9450.2.dn $$\chi_{9450}(1049, \cdot)$$ n/a 2592 6
9450.2.dp $$\chi_{9450}(101, \cdot)$$ n/a 2736 6
9450.2.ds $$\chi_{9450}(433, \cdot)$$ n/a 2560 8
9450.2.dv $$\chi_{9450}(323, \cdot)$$ n/a 1920 8
9450.2.dx $$\chi_{9450}(289, \cdot)$$ n/a 1920 8
9450.2.dz $$\chi_{9450}(269, \cdot)$$ n/a 2560 8
9450.2.ec $$\chi_{9450}(881, \cdot)$$ n/a 1920 8
9450.2.ed $$\chi_{9450}(341, \cdot)$$ n/a 1920 8
9450.2.ef $$\chi_{9450}(719, \cdot)$$ n/a 1920 8
9450.2.ei $$\chi_{9450}(629, \cdot)$$ n/a 1920 8
9450.2.ej $$\chi_{9450}(971, \cdot)$$ n/a 2560 8
9450.2.en $$\chi_{9450}(1369, \cdot)$$ n/a 1920 8
9450.2.eo $$\chi_{9450}(1009, \cdot)$$ n/a 1440 8
9450.2.et $$\chi_{9450}(109, \cdot)$$ n/a 2560 8
9450.2.eu $$\chi_{9450}(3041, \cdot)$$ n/a 1920 8
9450.2.ew $$\chi_{9450}(89, \cdot)$$ n/a 1920 8
9450.2.ez $$\chi_{9450}(893, \cdot)$$ n/a 5184 12
9450.2.fa $$\chi_{9450}(643, \cdot)$$ n/a 5184 12
9450.2.fb $$\chi_{9450}(157, \cdot)$$ n/a 5184 12
9450.2.fg $$\chi_{9450}(407, \cdot)$$ n/a 3888 12
9450.2.fh $$\chi_{9450}(443, \cdot)$$ n/a 5184 12
9450.2.fi $$\chi_{9450}(493, \cdot)$$ n/a 5184 12
9450.2.fk $$\chi_{9450}(121, \cdot)$$ n/a 17280 24
9450.2.fl $$\chi_{9450}(331, \cdot)$$ n/a 17280 24
9450.2.fm $$\chi_{9450}(211, \cdot)$$ n/a 12960 24
9450.2.fo $$\chi_{9450}(397, \cdot)$$ n/a 3840 16
9450.2.fq $$\chi_{9450}(53, \cdot)$$ n/a 5120 16
9450.2.fr $$\chi_{9450}(233, \cdot)$$ n/a 3840 16
9450.2.fu $$\chi_{9450}(197, \cdot)$$ n/a 2880 16
9450.2.fv $$\chi_{9450}(937, \cdot)$$ n/a 3840 16
9450.2.fy $$\chi_{9450}(73, \cdot)$$ n/a 3840 16
9450.2.fz $$\chi_{9450}(703, \cdot)$$ n/a 5120 16
9450.2.gb $$\chi_{9450}(737, \cdot)$$ n/a 3840 16
9450.2.gf $$\chi_{9450}(131, \cdot)$$ n/a 17280 24
9450.2.gh $$\chi_{9450}(209, \cdot)$$ n/a 17280 24
9450.2.gj $$\chi_{9450}(59, \cdot)$$ n/a 17280 24
9450.2.gl $$\chi_{9450}(169, \cdot)$$ n/a 12960 24
9450.2.gn $$\chi_{9450}(79, \cdot)$$ n/a 17280 24
9450.2.go $$\chi_{9450}(311, \cdot)$$ n/a 17280 24
9450.2.gq $$\chi_{9450}(41, \cdot)$$ n/a 17280 24
9450.2.gu $$\chi_{9450}(529, \cdot)$$ n/a 17280 24
9450.2.gw $$\chi_{9450}(479, \cdot)$$ n/a 17280 24
9450.2.gz $$\chi_{9450}(103, \cdot)$$ n/a 34560 48
9450.2.ha $$\chi_{9450}(317, \cdot)$$ n/a 34560 48
9450.2.hb $$\chi_{9450}(113, \cdot)$$ n/a 25920 48
9450.2.hg $$\chi_{9450}(187, \cdot)$$ n/a 34560 48
9450.2.hh $$\chi_{9450}(13, \cdot)$$ n/a 34560 48
9450.2.hi $$\chi_{9450}(23, \cdot)$$ n/a 34560 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9450))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9450)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(378))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(630))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(675))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(945))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1050))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1350))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1575))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1890))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3150))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4725))$$$$^{\oplus 2}$$