Properties

Label 7350.2
Level 7350
Weight 2
Dimension 312029
Nonzero newspaces 48
Sturm bound 5644800

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Defining parameters

Level: \( N \) = \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5644800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7350))\).

Total New Old
Modular forms 1424640 312029 1112611
Cusp forms 1397761 312029 1085732
Eisenstein series 26879 0 26879

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7350))\)

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
7350.2.a \(\chi_{7350}(1, \cdot)\) 7350.2.a.a 1 1
7350.2.a.b 1
7350.2.a.c 1
7350.2.a.d 1
7350.2.a.e 1
7350.2.a.f 1
7350.2.a.g 1
7350.2.a.h 1
7350.2.a.i 1
7350.2.a.j 1
7350.2.a.k 1
7350.2.a.l 1
7350.2.a.m 1
7350.2.a.n 1
7350.2.a.o 1
7350.2.a.p 1
7350.2.a.q 1
7350.2.a.r 1
7350.2.a.s 1
7350.2.a.t 1
7350.2.a.u 1
7350.2.a.v 1
7350.2.a.w 1
7350.2.a.x 1
7350.2.a.y 1
7350.2.a.z 1
7350.2.a.ba 1
7350.2.a.bb 1
7350.2.a.bc 1
7350.2.a.bd 1
7350.2.a.be 1
7350.2.a.bf 1
7350.2.a.bg 1
7350.2.a.bh 1
7350.2.a.bi 1
7350.2.a.bj 1
7350.2.a.bk 1
7350.2.a.bl 1
7350.2.a.bm 1
7350.2.a.bn 1
7350.2.a.bo 1
7350.2.a.bp 1
7350.2.a.bq 1
7350.2.a.br 1
7350.2.a.bs 1
7350.2.a.bt 1
7350.2.a.bu 1
7350.2.a.bv 1
7350.2.a.bw 1
7350.2.a.bx 1
7350.2.a.by 1
7350.2.a.bz 1
7350.2.a.ca 1
7350.2.a.cb 1
7350.2.a.cc 1
7350.2.a.cd 1
7350.2.a.ce 1
7350.2.a.cf 1
7350.2.a.cg 1
7350.2.a.ch 1
7350.2.a.ci 1
7350.2.a.cj 1
7350.2.a.ck 1
7350.2.a.cl 1
7350.2.a.cm 1
7350.2.a.cn 1
7350.2.a.co 1
7350.2.a.cp 1
7350.2.a.cq 1
7350.2.a.cr 1
7350.2.a.cs 1
7350.2.a.ct 1
7350.2.a.cu 1
7350.2.a.cv 1
7350.2.a.cw 1
7350.2.a.cx 1
7350.2.a.cy 1
7350.2.a.cz 1
7350.2.a.da 1
7350.2.a.db 2
7350.2.a.dc 2
7350.2.a.dd 2
7350.2.a.de 2
7350.2.a.df 2
7350.2.a.dg 2
7350.2.a.dh 2
7350.2.a.di 2
7350.2.a.dj 2
7350.2.a.dk 2
7350.2.a.dl 2
7350.2.a.dm 2
7350.2.a.dn 3
7350.2.a.do 3
7350.2.a.dp 3
7350.2.a.dq 3
7350.2.a.dr 4
7350.2.a.ds 4
7350.2.a.dt 4
7350.2.a.du 4
7350.2.b \(\chi_{7350}(2351, \cdot)\) n/a 252 1
7350.2.d \(\chi_{7350}(7349, \cdot)\) n/a 240 1
7350.2.g \(\chi_{7350}(4999, \cdot)\) n/a 122 1
7350.2.i \(\chi_{7350}(3301, \cdot)\) n/a 252 2
7350.2.j \(\chi_{7350}(2843, \cdot)\) n/a 492 2
7350.2.m \(\chi_{7350}(2743, \cdot)\) n/a 240 2
7350.2.n \(\chi_{7350}(1471, \cdot)\) n/a 816 4
7350.2.o \(\chi_{7350}(949, \cdot)\) n/a 240 2
7350.2.s \(\chi_{7350}(5801, \cdot)\) n/a 508 2
7350.2.u \(\chi_{7350}(3449, \cdot)\) n/a 480 2
7350.2.v \(\chi_{7350}(1051, \cdot)\) n/a 1056 6
7350.2.x \(\chi_{7350}(589, \cdot)\) n/a 824 4
7350.2.ba \(\chi_{7350}(1469, \cdot)\) n/a 1600 4
7350.2.bc \(\chi_{7350}(881, \cdot)\) n/a 1600 4
7350.2.bd \(\chi_{7350}(607, \cdot)\) n/a 480 4
7350.2.bg \(\chi_{7350}(557, \cdot)\) n/a 960 4
7350.2.bj \(\chi_{7350}(799, \cdot)\) n/a 1008 6
7350.2.bk \(\chi_{7350}(1049, \cdot)\) n/a 2016 6
7350.2.bm \(\chi_{7350}(251, \cdot)\) n/a 2136 6
7350.2.bo \(\chi_{7350}(361, \cdot)\) n/a 1600 8
7350.2.bp \(\chi_{7350}(97, \cdot)\) n/a 1600 8
7350.2.bs \(\chi_{7350}(197, \cdot)\) n/a 3280 8
7350.2.bt \(\chi_{7350}(151, \cdot)\) n/a 2136 12
7350.2.bv \(\chi_{7350}(307, \cdot)\) n/a 2016 12
7350.2.bw \(\chi_{7350}(407, \cdot)\) n/a 4032 12
7350.2.by \(\chi_{7350}(509, \cdot)\) n/a 3200 8
7350.2.ca \(\chi_{7350}(521, \cdot)\) n/a 3200 8
7350.2.ce \(\chi_{7350}(79, \cdot)\) n/a 1600 8
7350.2.cf \(\chi_{7350}(211, \cdot)\) n/a 6720 24
7350.2.ch \(\chi_{7350}(299, \cdot)\) n/a 4032 12
7350.2.cj \(\chi_{7350}(101, \cdot)\) n/a 4248 12
7350.2.cl \(\chi_{7350}(499, \cdot)\) n/a 2016 12
7350.2.cn \(\chi_{7350}(263, \cdot)\) n/a 6400 16
7350.2.cq \(\chi_{7350}(313, \cdot)\) n/a 3200 16
7350.2.cs \(\chi_{7350}(41, \cdot)\) n/a 13440 24
7350.2.cu \(\chi_{7350}(209, \cdot)\) n/a 13440 24
7350.2.cv \(\chi_{7350}(169, \cdot)\) n/a 6720 24
7350.2.cz \(\chi_{7350}(107, \cdot)\) n/a 8064 24
7350.2.da \(\chi_{7350}(157, \cdot)\) n/a 4032 24
7350.2.dc \(\chi_{7350}(121, \cdot)\) n/a 13440 48
7350.2.de \(\chi_{7350}(113, \cdot)\) n/a 26880 48
7350.2.df \(\chi_{7350}(13, \cdot)\) n/a 13440 48
7350.2.di \(\chi_{7350}(109, \cdot)\) n/a 13440 48
7350.2.dk \(\chi_{7350}(131, \cdot)\) n/a 26880 48
7350.2.dm \(\chi_{7350}(59, \cdot)\) n/a 26880 48
7350.2.dp \(\chi_{7350}(73, \cdot)\) n/a 26880 96
7350.2.dq \(\chi_{7350}(23, \cdot)\) n/a 53760 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7350))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7350)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3675))\)\(^{\oplus 2}\)