# Properties

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

## 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

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