# Properties

 Label 8670.2 Level 8670 Weight 2 Dimension 454616 Nonzero newspaces 36 Sturm bound 7990272

## Defining parameters

 Level: $$N$$ = $$8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$7990272$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8670))$$.

Total New Old
Modular forms 2010368 454616 1555752
Cusp forms 1984769 454616 1530153
Eisenstein series 25599 0 25599

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8670))$$

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
8670.2.a $$\chi_{8670}(1, \cdot)$$ 8670.2.a.a 1 1
8670.2.a.b 1
8670.2.a.c 1
8670.2.a.d 1
8670.2.a.e 1
8670.2.a.f 1
8670.2.a.g 1
8670.2.a.h 1
8670.2.a.i 1
8670.2.a.j 1
8670.2.a.k 1
8670.2.a.l 1
8670.2.a.m 1
8670.2.a.n 1
8670.2.a.o 1
8670.2.a.p 1
8670.2.a.q 1
8670.2.a.r 1
8670.2.a.s 1
8670.2.a.t 1
8670.2.a.u 1
8670.2.a.v 1
8670.2.a.w 1
8670.2.a.x 1
8670.2.a.y 1
8670.2.a.z 1
8670.2.a.ba 1
8670.2.a.bb 1
8670.2.a.bc 2
8670.2.a.bd 2
8670.2.a.be 2
8670.2.a.bf 2
8670.2.a.bg 2
8670.2.a.bh 2
8670.2.a.bi 2
8670.2.a.bj 2
8670.2.a.bk 2
8670.2.a.bl 3
8670.2.a.bm 3
8670.2.a.bn 3
8670.2.a.bo 3
8670.2.a.bp 3
8670.2.a.bq 3
8670.2.a.br 3
8670.2.a.bs 3
8670.2.a.bt 4
8670.2.a.bu 4
8670.2.a.bv 4
8670.2.a.bw 4
8670.2.a.bx 4
8670.2.a.by 4
8670.2.a.bz 4
8670.2.a.ca 4
8670.2.a.cb 6
8670.2.a.cc 6
8670.2.a.cd 6
8670.2.a.ce 6
8670.2.a.cf 6
8670.2.a.cg 6
8670.2.a.ch 6
8670.2.a.ci 6
8670.2.a.cj 8
8670.2.a.ck 8
8670.2.a.cl 8
8670.2.a.cm 8
8670.2.c $$\chi_{8670}(2311, \cdot)$$ n/a 180 1
8670.2.d $$\chi_{8670}(3469, \cdot)$$ n/a 270 1
8670.2.f $$\chi_{8670}(5779, \cdot)$$ n/a 268 1
8670.2.i $$\chi_{8670}(5453, \cdot)$$ n/a 1080 2
8670.2.l $$\chi_{8670}(1157, \cdot)$$ n/a 1084 2
8670.2.m $$\chi_{8670}(829, \cdot)$$ n/a 536 2
8670.2.p $$\chi_{8670}(4951, \cdot)$$ n/a 360 2
8670.2.q $$\chi_{8670}(1733, \cdot)$$ n/a 1080 2
8670.2.t $$\chi_{8670}(4373, \cdot)$$ n/a 1080 2
8670.2.u $$\chi_{8670}(2491, \cdot)$$ n/a 720 4
8670.2.w $$\chi_{8670}(1913, \cdot)$$ n/a 2160 4
8670.2.z $$\chi_{8670}(977, \cdot)$$ n/a 2160 4
8670.2.bb $$\chi_{8670}(1579, \cdot)$$ n/a 1088 4
8670.2.bd $$\chi_{8670}(643, \cdot)$$ n/a 2160 8
8670.2.bf $$\chi_{8670}(131, \cdot)$$ n/a 2880 8
8670.2.bh $$\chi_{8670}(329, \cdot)$$ n/a 4320 8
8670.2.bi $$\chi_{8670}(2377, \cdot)$$ n/a 2160 8
8670.2.bk $$\chi_{8670}(511, \cdot)$$ n/a 3264 16
8670.2.bn $$\chi_{8670}(169, \cdot)$$ n/a 4928 16
8670.2.bp $$\chi_{8670}(409, \cdot)$$ n/a 4928 16
8670.2.bq $$\chi_{8670}(271, \cdot)$$ n/a 3264 16
8670.2.bs $$\chi_{8670}(47, \cdot)$$ n/a 19584 32
8670.2.bv $$\chi_{8670}(203, \cdot)$$ n/a 19584 32
8670.2.bw $$\chi_{8670}(361, \cdot)$$ n/a 6528 32
8670.2.bz $$\chi_{8670}(259, \cdot)$$ n/a 9856 32
8670.2.ca $$\chi_{8670}(137, \cdot)$$ n/a 19584 32
8670.2.cd $$\chi_{8670}(353, \cdot)$$ n/a 19584 32
8670.2.ce $$\chi_{8670}(19, \cdot)$$ n/a 19456 64
8670.2.cg $$\chi_{8670}(53, \cdot)$$ n/a 39168 64
8670.2.cj $$\chi_{8670}(257, \cdot)$$ n/a 39168 64
8670.2.cl $$\chi_{8670}(121, \cdot)$$ n/a 13056 64
8670.2.cn $$\chi_{8670}(37, \cdot)$$ n/a 39168 128
8670.2.co $$\chi_{8670}(29, \cdot)$$ n/a 78336 128
8670.2.cq $$\chi_{8670}(11, \cdot)$$ n/a 52224 128
8670.2.cs $$\chi_{8670}(7, \cdot)$$ n/a 39168 128

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8670))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8670)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(170))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(255))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(289))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(510))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(578))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(867))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1445))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1734))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2890))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4335))$$$$^{\oplus 2}$$