## Defining parameters

 Level: $$N$$ = $$7935 = 3 \cdot 5 \cdot 23^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$8937984$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7935))$$.

Total New Old
Modular forms 2246464 1534640 711824
Cusp forms 2222529 1526184 696345
Eisenstein series 23935 8456 15479

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7935))$$

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
7935.2.a $$\chi_{7935}(1, \cdot)$$ 7935.2.a.a 1 1
7935.2.a.b 1
7935.2.a.c 1
7935.2.a.d 1
7935.2.a.e 1
7935.2.a.f 1
7935.2.a.g 1
7935.2.a.h 1
7935.2.a.i 1
7935.2.a.j 1
7935.2.a.k 1
7935.2.a.l 1
7935.2.a.m 1
7935.2.a.n 2
7935.2.a.o 2
7935.2.a.p 2
7935.2.a.q 2
7935.2.a.r 2
7935.2.a.s 2
7935.2.a.t 2
7935.2.a.u 3
7935.2.a.v 3
7935.2.a.w 3
7935.2.a.x 3
7935.2.a.y 3
7935.2.a.z 4
7935.2.a.ba 4
7935.2.a.bb 5
7935.2.a.bc 5
7935.2.a.bd 6
7935.2.a.be 6
7935.2.a.bf 6
7935.2.a.bg 6
7935.2.a.bh 8
7935.2.a.bi 8
7935.2.a.bj 10
7935.2.a.bk 10
7935.2.a.bl 12
7935.2.a.bm 12
7935.2.a.bn 15
7935.2.a.bo 15
7935.2.a.bp 15
7935.2.a.bq 15
7935.2.a.br 16
7935.2.a.bs 16
7935.2.a.bt 25
7935.2.a.bu 25
7935.2.a.bv 25
7935.2.a.bw 25
7935.2.b $$\chi_{7935}(6349, \cdot)$$ n/a 504 1
7935.2.c $$\chi_{7935}(1586, \cdot)$$ n/a 672 1
7935.2.h $$\chi_{7935}(7934, \cdot)$$ n/a 968 1
7935.2.i $$\chi_{7935}(2117, \cdot)$$ n/a 1936 2
7935.2.j $$\chi_{7935}(1057, \cdot)$$ n/a 1008 2
7935.2.m $$\chi_{7935}(466, \cdot)$$ n/a 3360 10
7935.2.n $$\chi_{7935}(359, \cdot)$$ n/a 9680 10
7935.2.s $$\chi_{7935}(881, \cdot)$$ n/a 6720 10
7935.2.t $$\chi_{7935}(334, \cdot)$$ n/a 5040 10
7935.2.u $$\chi_{7935}(346, \cdot)$$ n/a 8096 22
7935.2.x $$\chi_{7935}(28, \cdot)$$ n/a 10080 20
7935.2.y $$\chi_{7935}(647, \cdot)$$ n/a 19360 20
7935.2.z $$\chi_{7935}(344, \cdot)$$ n/a 24200 22
7935.2.be $$\chi_{7935}(206, \cdot)$$ n/a 16192 22
7935.2.bf $$\chi_{7935}(139, \cdot)$$ n/a 12144 22
7935.2.bi $$\chi_{7935}(22, \cdot)$$ n/a 24288 44
7935.2.bj $$\chi_{7935}(47, \cdot)$$ n/a 48400 44
7935.2.bk $$\chi_{7935}(16, \cdot)$$ n/a 80960 220
7935.2.bl $$\chi_{7935}(4, \cdot)$$ n/a 121440 220
7935.2.bm $$\chi_{7935}(11, \cdot)$$ n/a 161920 220
7935.2.br $$\chi_{7935}(14, \cdot)$$ n/a 242000 220
7935.2.bs $$\chi_{7935}(2, \cdot)$$ n/a 484000 440
7935.2.bt $$\chi_{7935}(7, \cdot)$$ n/a 242880 440

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7935))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7935)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(529))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1587))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2645))$$$$^{\oplus 2}$$