# Properties

 Label 8450.2 Level 8450 Weight 2 Dimension 646481 Nonzero newspaces 48 Sturm bound 8517600

## Defining parameters

 Level: $$N$$ = $$8450 = 2 \cdot 5^{2} \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$8517600$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8450))$$.

Total New Old
Modular forms 2142168 646481 1495687
Cusp forms 2116633 646481 1470152
Eisenstein series 25535 0 25535

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8450))$$

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
8450.2.a $$\chi_{8450}(1, \cdot)$$ 8450.2.a.a 1 1
8450.2.a.b 1
8450.2.a.c 1
8450.2.a.d 1
8450.2.a.e 1
8450.2.a.f 1
8450.2.a.g 1
8450.2.a.h 1
8450.2.a.i 1
8450.2.a.j 1
8450.2.a.k 1
8450.2.a.l 1
8450.2.a.m 1
8450.2.a.n 1
8450.2.a.o 1
8450.2.a.p 1
8450.2.a.q 1
8450.2.a.r 1
8450.2.a.s 1
8450.2.a.t 1
8450.2.a.u 1
8450.2.a.v 1
8450.2.a.w 1
8450.2.a.x 1
8450.2.a.y 1
8450.2.a.z 2
8450.2.a.ba 2
8450.2.a.bb 2
8450.2.a.bc 2
8450.2.a.bd 2
8450.2.a.be 2
8450.2.a.bf 2
8450.2.a.bg 2
8450.2.a.bh 2
8450.2.a.bi 2
8450.2.a.bj 2
8450.2.a.bk 2
8450.2.a.bl 2
8450.2.a.bm 2
8450.2.a.bn 3
8450.2.a.bo 3
8450.2.a.bp 3
8450.2.a.bq 3
8450.2.a.br 3
8450.2.a.bs 3
8450.2.a.bt 3
8450.2.a.bu 3
8450.2.a.bv 3
8450.2.a.bw 3
8450.2.a.bx 3
8450.2.a.by 3
8450.2.a.bz 3
8450.2.a.ca 3
8450.2.a.cb 3
8450.2.a.cc 3
8450.2.a.cd 3
8450.2.a.ce 3
8450.2.a.cf 3
8450.2.a.cg 3
8450.2.a.ch 4
8450.2.a.ci 4
8450.2.a.cj 4
8450.2.a.ck 4
8450.2.a.cl 4
8450.2.a.cm 4
8450.2.a.cn 4
8450.2.a.co 4
8450.2.a.cp 6
8450.2.a.cq 6
8450.2.a.cr 8
8450.2.a.cs 8
8450.2.a.ct 9
8450.2.a.cu 9
8450.2.a.cv 9
8450.2.a.cw 9
8450.2.a.cx 9
8450.2.a.cy 9
8450.2.a.cz 9
8450.2.a.da 9
8450.2.b $$\chi_{8450}(7099, \cdot)$$ n/a 232 1
8450.2.c $$\chi_{8450}(8449, \cdot)$$ n/a 232 1
8450.2.d $$\chi_{8450}(1351, \cdot)$$ n/a 242 1
8450.2.e $$\chi_{8450}(6951, \cdot)$$ n/a 490 2
8450.2.g $$\chi_{8450}(3957, \cdot)$$ n/a 462 2
8450.2.j $$\chi_{8450}(2943, \cdot)$$ n/a 462 2
8450.2.l $$\chi_{8450}(1691, \cdot)$$ n/a 1548 4
8450.2.m $$\chi_{8450}(2051, \cdot)$$ n/a 488 2
8450.2.n $$\chi_{8450}(699, \cdot)$$ n/a 464 2
8450.2.o $$\chi_{8450}(5599, \cdot)$$ n/a 460 2
8450.2.p $$\chi_{8450}(3041, \cdot)$$ n/a 1544 4
8450.2.q $$\chi_{8450}(339, \cdot)$$ n/a 1552 4
8450.2.r $$\chi_{8450}(1689, \cdot)$$ n/a 1536 4
8450.2.t $$\chi_{8450}(657, \cdot)$$ n/a 924 4
8450.2.w $$\chi_{8450}(357, \cdot)$$ n/a 924 4
8450.2.y $$\chi_{8450}(651, \cdot)$$ n/a 3468 12
8450.2.z $$\chi_{8450}(191, \cdot)$$ n/a 3072 8
8450.2.bb $$\chi_{8450}(577, \cdot)$$ n/a 3080 8
8450.2.be $$\chi_{8450}(437, \cdot)$$ n/a 3080 8
8450.2.bg $$\chi_{8450}(51, \cdot)$$ n/a 3480 12
8450.2.bh $$\chi_{8450}(649, \cdot)$$ n/a 3264 12
8450.2.bi $$\chi_{8450}(599, \cdot)$$ n/a 3288 12
8450.2.bj $$\chi_{8450}(2389, \cdot)$$ n/a 3072 8
8450.2.bk $$\chi_{8450}(529, \cdot)$$ n/a 3088 8
8450.2.bl $$\chi_{8450}(361, \cdot)$$ n/a 3088 8
8450.2.bm $$\chi_{8450}(451, \cdot)$$ n/a 6888 24
8450.2.bo $$\chi_{8450}(307, \cdot)$$ n/a 6552 24
8450.2.br $$\chi_{8450}(57, \cdot)$$ n/a 6552 24
8450.2.bu $$\chi_{8450}(427, \cdot)$$ n/a 6160 16
8450.2.bx $$\chi_{8450}(587, \cdot)$$ n/a 6160 16
8450.2.bz $$\chi_{8450}(131, \cdot)$$ n/a 21888 48
8450.2.ca $$\chi_{8450}(399, \cdot)$$ n/a 6576 24
8450.2.cb $$\chi_{8450}(49, \cdot)$$ n/a 6528 24
8450.2.cc $$\chi_{8450}(101, \cdot)$$ n/a 6912 24
8450.2.cd $$\chi_{8450}(129, \cdot)$$ n/a 21888 48
8450.2.ce $$\chi_{8450}(79, \cdot)$$ n/a 21792 48
8450.2.cf $$\chi_{8450}(181, \cdot)$$ n/a 21792 48
8450.2.ch $$\chi_{8450}(193, \cdot)$$ n/a 13104 48
8450.2.ck $$\chi_{8450}(7, \cdot)$$ n/a 13104 48
8450.2.cm $$\chi_{8450}(61, \cdot)$$ n/a 43776 96
8450.2.co $$\chi_{8450}(47, \cdot)$$ n/a 43680 96
8450.2.cr $$\chi_{8450}(73, \cdot)$$ n/a 43680 96
8450.2.ct $$\chi_{8450}(121, \cdot)$$ n/a 43584 96
8450.2.cu $$\chi_{8450}(9, \cdot)$$ n/a 43584 96
8450.2.cv $$\chi_{8450}(69, \cdot)$$ n/a 43776 96
8450.2.cx $$\chi_{8450}(33, \cdot)$$ n/a 87360 192
8450.2.da $$\chi_{8450}(37, \cdot)$$ n/a 87360 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8450))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8450)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(650))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1690))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4225))$$$$^{\oplus 2}$$