# Properties

 Label 8470.2 Level 8470 Weight 2 Dimension 602186 Nonzero newspaces 48 Sturm bound 8363520

## Defining parameters

 Level: $$N$$ = $$8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$8363520$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8470))$$.

Total New Old
Modular forms 2106240 602186 1504054
Cusp forms 2075521 602186 1473335
Eisenstein series 30719 0 30719

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8470))$$

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
8470.2.a $$\chi_{8470}(1, \cdot)$$ 8470.2.a.a 1 1
8470.2.a.b 1
8470.2.a.c 1
8470.2.a.d 1
8470.2.a.e 1
8470.2.a.f 1
8470.2.a.g 1
8470.2.a.h 1
8470.2.a.i 1
8470.2.a.j 1
8470.2.a.k 1
8470.2.a.l 1
8470.2.a.m 1
8470.2.a.n 1
8470.2.a.o 1
8470.2.a.p 1
8470.2.a.q 1
8470.2.a.r 1
8470.2.a.s 1
8470.2.a.t 1
8470.2.a.u 1
8470.2.a.v 1
8470.2.a.w 1
8470.2.a.x 1
8470.2.a.y 1
8470.2.a.z 1
8470.2.a.ba 1
8470.2.a.bb 1
8470.2.a.bc 1
8470.2.a.bd 1
8470.2.a.be 1
8470.2.a.bf 1
8470.2.a.bg 1
8470.2.a.bh 1
8470.2.a.bi 2
8470.2.a.bj 2
8470.2.a.bk 2
8470.2.a.bl 2
8470.2.a.bm 2
8470.2.a.bn 2
8470.2.a.bo 2
8470.2.a.bp 2
8470.2.a.bq 2
8470.2.a.br 2
8470.2.a.bs 2
8470.2.a.bt 2
8470.2.a.bu 2
8470.2.a.bv 2
8470.2.a.bw 2
8470.2.a.bx 2
8470.2.a.by 2
8470.2.a.bz 2
8470.2.a.ca 2
8470.2.a.cb 2
8470.2.a.cc 2
8470.2.a.cd 2
8470.2.a.ce 2
8470.2.a.cf 2
8470.2.a.cg 3
8470.2.a.ch 3
8470.2.a.ci 3
8470.2.a.cj 3
8470.2.a.ck 3
8470.2.a.cl 3
8470.2.a.cm 3
8470.2.a.cn 3
8470.2.a.co 4
8470.2.a.cp 4
8470.2.a.cq 4
8470.2.a.cr 4
8470.2.a.cs 4
8470.2.a.ct 4
8470.2.a.cu 6
8470.2.a.cv 6
8470.2.a.cw 6
8470.2.a.cx 6
8470.2.a.cy 6
8470.2.a.cz 6
8470.2.a.da 6
8470.2.a.db 6
8470.2.a.dc 6
8470.2.a.dd 6
8470.2.a.de 6
8470.2.a.df 6
8470.2.a.dg 8
8470.2.a.dh 8
8470.2.c $$\chi_{8470}(3389, \cdot)$$ n/a 328 1
8470.2.e $$\chi_{8470}(5081, \cdot)$$ n/a 288 1
8470.2.g $$\chi_{8470}(8469, \cdot)$$ n/a 432 1
8470.2.i $$\chi_{8470}(4841, \cdot)$$ n/a 584 2
8470.2.l $$\chi_{8470}(727, \cdot)$$ n/a 872 2
8470.2.m $$\chi_{8470}(967, \cdot)$$ n/a 648 2
8470.2.n $$\chi_{8470}(3711, \cdot)$$ n/a 864 4
8470.2.o $$\chi_{8470}(1209, \cdot)$$ n/a 864 2
8470.2.r $$\chi_{8470}(2179, \cdot)$$ n/a 872 2
8470.2.t $$\chi_{8470}(241, \cdot)$$ n/a 576 2
8470.2.w $$\chi_{8470}(699, \cdot)$$ n/a 1728 4
8470.2.y $$\chi_{8470}(1371, \cdot)$$ n/a 1152 4
8470.2.ba $$\chi_{8470}(729, \cdot)$$ n/a 1296 4
8470.2.bc $$\chi_{8470}(771, \cdot)$$ n/a 2640 10
8470.2.bd $$\chi_{8470}(243, \cdot)$$ n/a 1744 4
8470.2.be $$\chi_{8470}(4113, \cdot)$$ n/a 1728 4
8470.2.bh $$\chi_{8470}(81, \cdot)$$ n/a 2304 8
8470.2.bi $$\chi_{8470}(1443, \cdot)$$ n/a 2592 8
8470.2.bj $$\chi_{8470}(27, \cdot)$$ n/a 3456 8
8470.2.bm $$\chi_{8470}(461, \cdot)$$ n/a 3520 10
8470.2.bo $$\chi_{8470}(309, \cdot)$$ n/a 3960 10
8470.2.br $$\chi_{8470}(769, \cdot)$$ n/a 5280 10
8470.2.bu $$\chi_{8470}(481, \cdot)$$ n/a 2304 8
8470.2.bw $$\chi_{8470}(9, \cdot)$$ n/a 3456 8
8470.2.bz $$\chi_{8470}(1909, \cdot)$$ n/a 3456 8
8470.2.ca $$\chi_{8470}(221, \cdot)$$ n/a 7040 20
8470.2.cb $$\chi_{8470}(43, \cdot)$$ n/a 7920 20
8470.2.cc $$\chi_{8470}(573, \cdot)$$ n/a 10560 20
8470.2.cf $$\chi_{8470}(71, \cdot)$$ n/a 10560 40
8470.2.ci $$\chi_{8470}(233, \cdot)$$ n/a 6912 16
8470.2.cj $$\chi_{8470}(3, \cdot)$$ n/a 6912 16
8470.2.cm $$\chi_{8470}(439, \cdot)$$ n/a 10560 20
8470.2.co $$\chi_{8470}(131, \cdot)$$ n/a 7040 20
8470.2.cq $$\chi_{8470}(529, \cdot)$$ n/a 10560 20
8470.2.cs $$\chi_{8470}(139, \cdot)$$ n/a 21120 40
8470.2.cv $$\chi_{8470}(169, \cdot)$$ n/a 15840 40
8470.2.cx $$\chi_{8470}(41, \cdot)$$ n/a 14080 40
8470.2.da $$\chi_{8470}(263, \cdot)$$ n/a 21120 40
8470.2.db $$\chi_{8470}(353, \cdot)$$ n/a 21120 40
8470.2.dc $$\chi_{8470}(191, \cdot)$$ n/a 28160 80
8470.2.df $$\chi_{8470}(97, \cdot)$$ n/a 42240 80
8470.2.dg $$\chi_{8470}(57, \cdot)$$ n/a 31680 80
8470.2.dh $$\chi_{8470}(179, \cdot)$$ n/a 42240 80
8470.2.dj $$\chi_{8470}(61, \cdot)$$ n/a 28160 80
8470.2.dl $$\chi_{8470}(19, \cdot)$$ n/a 42240 80
8470.2.do $$\chi_{8470}(47, \cdot)$$ n/a 84480 160
8470.2.dp $$\chi_{8470}(107, \cdot)$$ n/a 84480 160

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8470))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8470)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(605))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(770))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(847))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1210))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1694))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4235))$$$$^{\oplus 2}$$