# Properties

 Label 5070.2 Level 5070 Weight 2 Dimension 154316 Nonzero newspaces 40 Sturm bound 2725632

## Defining parameters

 Level: $$N$$ = $$5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$2725632$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5070))$$.

Total New Old
Modular forms 688704 154316 534388
Cusp forms 674113 154316 519797
Eisenstein series 14591 0 14591

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5070))$$

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
5070.2.a $$\chi_{5070}(1, \cdot)$$ 5070.2.a.a 1 1
5070.2.a.b 1
5070.2.a.c 1
5070.2.a.d 1
5070.2.a.e 1
5070.2.a.f 1
5070.2.a.g 1
5070.2.a.h 1
5070.2.a.i 1
5070.2.a.j 1
5070.2.a.k 1
5070.2.a.l 1
5070.2.a.m 1
5070.2.a.n 1
5070.2.a.o 1
5070.2.a.p 1
5070.2.a.q 1
5070.2.a.r 1
5070.2.a.s 1
5070.2.a.t 1
5070.2.a.u 1
5070.2.a.v 1
5070.2.a.w 1
5070.2.a.x 1
5070.2.a.y 2
5070.2.a.z 2
5070.2.a.ba 2
5070.2.a.bb 2
5070.2.a.bc 2
5070.2.a.bd 2
5070.2.a.be 2
5070.2.a.bf 2
5070.2.a.bg 2
5070.2.a.bh 2
5070.2.a.bi 2
5070.2.a.bj 3
5070.2.a.bk 3
5070.2.a.bl 3
5070.2.a.bm 3
5070.2.a.bn 3
5070.2.a.bo 3
5070.2.a.bp 3
5070.2.a.bq 3
5070.2.a.br 3
5070.2.a.bs 3
5070.2.a.bt 3
5070.2.a.bu 3
5070.2.a.bv 3
5070.2.a.bw 3
5070.2.a.bx 3
5070.2.a.by 3
5070.2.a.bz 4
5070.2.a.ca 4
5070.2.b $$\chi_{5070}(1351, \cdot)$$ 5070.2.b.a 2 1
5070.2.b.b 2
5070.2.b.c 2
5070.2.b.d 2
5070.2.b.e 2
5070.2.b.f 2
5070.2.b.g 2
5070.2.b.h 2
5070.2.b.i 2
5070.2.b.j 2
5070.2.b.k 2
5070.2.b.l 2
5070.2.b.m 2
5070.2.b.n 2
5070.2.b.o 4
5070.2.b.p 4
5070.2.b.q 4
5070.2.b.r 4
5070.2.b.s 6
5070.2.b.t 6
5070.2.b.u 6
5070.2.b.v 6
5070.2.b.w 6
5070.2.b.x 6
5070.2.b.y 6
5070.2.b.z 6
5070.2.b.ba 8
5070.2.e $$\chi_{5070}(2029, \cdot)$$ n/a 154 1
5070.2.f $$\chi_{5070}(3379, \cdot)$$ n/a 156 1
5070.2.i $$\chi_{5070}(991, \cdot)$$ n/a 208 2
5070.2.j $$\chi_{5070}(577, \cdot)$$ n/a 308 2
5070.2.l $$\chi_{5070}(677, \cdot)$$ n/a 620 2
5070.2.n $$\chi_{5070}(239, \cdot)$$ n/a 616 2
5070.2.p $$\chi_{5070}(1451, \cdot)$$ n/a 416 2
5070.2.s $$\chi_{5070}(1013, \cdot)$$ n/a 616 2
5070.2.t $$\chi_{5070}(3817, \cdot)$$ n/a 308 2
5070.2.x $$\chi_{5070}(2389, \cdot)$$ n/a 312 2
5070.2.y $$\chi_{5070}(529, \cdot)$$ n/a 304 2
5070.2.bb $$\chi_{5070}(361, \cdot)$$ n/a 208 2
5070.2.bd $$\chi_{5070}(427, \cdot)$$ n/a 616 4
5070.2.be $$\chi_{5070}(23, \cdot)$$ n/a 1232 4
5070.2.bh $$\chi_{5070}(1601, \cdot)$$ n/a 816 4
5070.2.bj $$\chi_{5070}(89, \cdot)$$ n/a 1232 4
5070.2.bl $$\chi_{5070}(653, \cdot)$$ n/a 1232 4
5070.2.bn $$\chi_{5070}(1333, \cdot)$$ n/a 616 4
5070.2.bo $$\chi_{5070}(391, \cdot)$$ n/a 1488 12
5070.2.bq $$\chi_{5070}(259, \cdot)$$ n/a 2160 12
5070.2.bt $$\chi_{5070}(79, \cdot)$$ n/a 2208 12
5070.2.bu $$\chi_{5070}(181, \cdot)$$ n/a 1488 12
5070.2.bw $$\chi_{5070}(61, \cdot)$$ n/a 2880 24
5070.2.by $$\chi_{5070}(307, \cdot)$$ n/a 4368 24
5070.2.ca $$\chi_{5070}(77, \cdot)$$ n/a 8736 24
5070.2.cc $$\chi_{5070}(161, \cdot)$$ n/a 5760 24
5070.2.ce $$\chi_{5070}(359, \cdot)$$ n/a 8736 24
5070.2.cf $$\chi_{5070}(53, \cdot)$$ n/a 8736 24
5070.2.ci $$\chi_{5070}(73, \cdot)$$ n/a 4368 24
5070.2.ck $$\chi_{5070}(121, \cdot)$$ n/a 2880 24
5070.2.cl $$\chi_{5070}(139, \cdot)$$ n/a 4416 24
5070.2.co $$\chi_{5070}(49, \cdot)$$ n/a 4320 24
5070.2.cq $$\chi_{5070}(67, \cdot)$$ n/a 8736 48
5070.2.ct $$\chi_{5070}(107, \cdot)$$ n/a 17472 48
5070.2.cu $$\chi_{5070}(59, \cdot)$$ n/a 17472 48
5070.2.cw $$\chi_{5070}(11, \cdot)$$ n/a 11712 48
5070.2.cy $$\chi_{5070}(17, \cdot)$$ n/a 17472 48
5070.2.da $$\chi_{5070}(7, \cdot)$$ n/a 8736 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5070))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5070)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1014))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1690))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2535))$$$$^{\oplus 2}$$