Space of modular forms of level 7935 and weight 2

• Label: 7935.2
• Level: 7935
• Weight: 2
• Dimension: 1526184
• Nonzero newspaces: 24
• Sturm bound: 8937984

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

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