Properties

Label 9450.2
Level 9450
Weight 2
Dimension 542676
Nonzero newspaces 96
Sturm bound 9331200

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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

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