# Properties

 Label 5175.2 Level 5175 Weight 2 Dimension 686961 Nonzero newspaces 48 Sturm bound 3801600

## Defining parameters

 Level: $$N$$ = $$5175 = 3^{2} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$3801600$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5175))$$.

Total New Old
Modular forms 960256 694709 265547
Cusp forms 940545 686961 253584
Eisenstein series 19711 7748 11963

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5175))$$

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
5175.2.a $$\chi_{5175}(1, \cdot)$$ 5175.2.a.a 1 1
5175.2.a.b 1
5175.2.a.c 1
5175.2.a.d 1
5175.2.a.e 1
5175.2.a.f 1
5175.2.a.g 1
5175.2.a.h 1
5175.2.a.i 1
5175.2.a.j 1
5175.2.a.k 1
5175.2.a.l 1
5175.2.a.m 1
5175.2.a.n 1
5175.2.a.o 1
5175.2.a.p 1
5175.2.a.q 1
5175.2.a.r 1
5175.2.a.s 1
5175.2.a.t 1
5175.2.a.u 1
5175.2.a.v 1
5175.2.a.w 1
5175.2.a.x 1
5175.2.a.y 1
5175.2.a.z 1
5175.2.a.ba 2
5175.2.a.bb 2
5175.2.a.bc 2
5175.2.a.bd 2
5175.2.a.be 2
5175.2.a.bf 2
5175.2.a.bg 2
5175.2.a.bh 2
5175.2.a.bi 2
5175.2.a.bj 2
5175.2.a.bk 2
5175.2.a.bl 2
5175.2.a.bm 2
5175.2.a.bn 2
5175.2.a.bo 2
5175.2.a.bp 2
5175.2.a.bq 3
5175.2.a.br 3
5175.2.a.bs 3
5175.2.a.bt 3
5175.2.a.bu 3
5175.2.a.bv 4
5175.2.a.bw 4
5175.2.a.bx 4
5175.2.a.by 6
5175.2.a.bz 6
5175.2.a.ca 7
5175.2.a.cb 7
5175.2.a.cc 7
5175.2.a.cd 7
5175.2.a.ce 7
5175.2.a.cf 7
5175.2.a.cg 7
5175.2.a.ch 7
5175.2.a.ci 10
5175.2.a.cj 10
5175.2.b $$\chi_{5175}(2899, \cdot)$$ n/a 166 1
5175.2.c $$\chi_{5175}(2276, \cdot)$$ n/a 152 1
5175.2.h $$\chi_{5175}(5174, \cdot)$$ n/a 144 1
5175.2.i $$\chi_{5175}(1726, \cdot)$$ n/a 836 2
5175.2.j $$\chi_{5175}(2393, \cdot)$$ n/a 264 2
5175.2.k $$\chi_{5175}(2368, \cdot)$$ n/a 356 2
5175.2.n $$\chi_{5175}(1036, \cdot)$$ n/a 1104 4
5175.2.o $$\chi_{5175}(1724, \cdot)$$ n/a 856 2
5175.2.t $$\chi_{5175}(551, \cdot)$$ n/a 900 2
5175.2.u $$\chi_{5175}(1174, \cdot)$$ n/a 792 2
5175.2.x $$\chi_{5175}(1034, \cdot)$$ n/a 960 4
5175.2.y $$\chi_{5175}(206, \cdot)$$ n/a 960 4
5175.2.z $$\chi_{5175}(829, \cdot)$$ n/a 1096 4
5175.2.bc $$\chi_{5175}(676, \cdot)$$ n/a 1870 10
5175.2.bf $$\chi_{5175}(668, \cdot)$$ n/a 1584 4
5175.2.bg $$\chi_{5175}(643, \cdot)$$ n/a 1712 4
5175.2.bh $$\chi_{5175}(346, \cdot)$$ n/a 5280 8
5175.2.bk $$\chi_{5175}(298, \cdot)$$ n/a 2384 8
5175.2.bl $$\chi_{5175}(323, \cdot)$$ n/a 1760 8
5175.2.bm $$\chi_{5175}(224, \cdot)$$ n/a 1440 10
5175.2.br $$\chi_{5175}(251, \cdot)$$ n/a 1520 10
5175.2.bs $$\chi_{5175}(1099, \cdot)$$ n/a 1780 10
5175.2.bv $$\chi_{5175}(139, \cdot)$$ n/a 5280 8
5175.2.bw $$\chi_{5175}(896, \cdot)$$ n/a 5728 8
5175.2.bx $$\chi_{5175}(344, \cdot)$$ n/a 5728 8
5175.2.ca $$\chi_{5175}(151, \cdot)$$ n/a 9000 20
5175.2.cd $$\chi_{5175}(343, \cdot)$$ n/a 3560 20
5175.2.ce $$\chi_{5175}(593, \cdot)$$ n/a 2880 20
5175.2.cf $$\chi_{5175}(271, \cdot)$$ n/a 11920 40
5175.2.cg $$\chi_{5175}(22, \cdot)$$ n/a 11456 16
5175.2.ch $$\chi_{5175}(47, \cdot)$$ n/a 10560 16
5175.2.ck $$\chi_{5175}(49, \cdot)$$ n/a 8560 20
5175.2.cl $$\chi_{5175}(176, \cdot)$$ n/a 9000 20
5175.2.cq $$\chi_{5175}(74, \cdot)$$ n/a 8560 20
5175.2.ct $$\chi_{5175}(64, \cdot)$$ n/a 11920 40
5175.2.cu $$\chi_{5175}(296, \cdot)$$ n/a 9600 40
5175.2.cv $$\chi_{5175}(44, \cdot)$$ n/a 9600 40
5175.2.cy $$\chi_{5175}(7, \cdot)$$ n/a 17120 40
5175.2.cz $$\chi_{5175}(32, \cdot)$$ n/a 17120 40
5175.2.dc $$\chi_{5175}(16, \cdot)$$ n/a 57280 80
5175.2.dd $$\chi_{5175}(8, \cdot)$$ n/a 19200 80
5175.2.de $$\chi_{5175}(28, \cdot)$$ n/a 23840 80
5175.2.dj $$\chi_{5175}(14, \cdot)$$ n/a 57280 80
5175.2.dk $$\chi_{5175}(11, \cdot)$$ n/a 57280 80
5175.2.dl $$\chi_{5175}(4, \cdot)$$ n/a 57280 80
5175.2.dq $$\chi_{5175}(2, \cdot)$$ n/a 114560 160
5175.2.dr $$\chi_{5175}(67, \cdot)$$ n/a 114560 160

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5175))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5175)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1035))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1725))$$$$^{\oplus 2}$$