Space of modular forms of level 4815 and weight 2

• Label: 4815.2
• Level: 4815
• Weight: 2
• Dimension: 595218
• Nonzero newspaces: 24
• Sturm bound: 3297024

Defining parameters

Level:	\( N \)	=	\( 4815 = 3^{2} \cdot 5 \cdot 107 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(3297024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4815))\).

	Total	New	Old
Modular forms	831040	600890	230150
Cusp forms	817473	595218	222255
Eisenstein series	13567	5672	7895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4815))\)

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 available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
4815.2.a	\(\chi_{4815}(1, \cdot)\)	4815.2.a.a	1	1
		4815.2.a.b	1
		4815.2.a.c	1
		4815.2.a.d	1
		4815.2.a.e	1
		4815.2.a.f	1
		4815.2.a.g	1
		4815.2.a.h	3
		4815.2.a.i	3
		4815.2.a.j	4
		4815.2.a.k	5
		4815.2.a.l	5
		4815.2.a.m	5
		4815.2.a.n	8
		4815.2.a.o	9
		4815.2.a.p	10
		4815.2.a.q	11
		4815.2.a.r	11
		4815.2.a.s	11
		4815.2.a.t	11
		4815.2.a.u	12
		4815.2.a.v	15
		4815.2.a.w	24
		4815.2.a.x	24
4815.2.b	\(\chi_{4815}(964, \cdot)\)	n/a	264	1
4815.2.d	\(\chi_{4815}(4814, \cdot)\)	n/a	216	1
4815.2.g	\(\chi_{4815}(3851, \cdot)\)	n/a	144	1
4815.2.i	\(\chi_{4815}(1606, \cdot)\)	n/a	848	2
4815.2.j	\(\chi_{4815}(1178, \cdot)\)	n/a	424	2
4815.2.l	\(\chi_{4815}(748, \cdot)\)	n/a	536	2
4815.2.o	\(\chi_{4815}(641, \cdot)\)	n/a	864	2
4815.2.r	\(\chi_{4815}(1604, \cdot)\)	n/a	1288	2
4815.2.t	\(\chi_{4815}(2569, \cdot)\)	n/a	1272	2
4815.2.u	\(\chi_{4815}(427, \cdot)\)	n/a	2576	4
4815.2.w	\(\chi_{4815}(857, \cdot)\)	n/a	2544	4
4815.2.y	\(\chi_{4815}(136, \cdot)\)	n/a	9360	52
4815.2.ba	\(\chi_{4815}(26, \cdot)\)	n/a	7488	52
4815.2.bd	\(\chi_{4815}(179, \cdot)\)	n/a	11232	52
4815.2.bf	\(\chi_{4815}(19, \cdot)\)	n/a	13936	52
4815.2.bg	\(\chi_{4815}(16, \cdot)\)	n/a	44928	104
4815.2.bi	\(\chi_{4815}(28, \cdot)\)	n/a	27872	104
4815.2.bk	\(\chi_{4815}(53, \cdot)\)	n/a	22464	104
4815.2.bl	\(\chi_{4815}(4, \cdot)\)	n/a	66976	104
4815.2.bn	\(\chi_{4815}(59, \cdot)\)	n/a	66976	104
4815.2.bq	\(\chi_{4815}(131, \cdot)\)	n/a	44928	104
4815.2.bt	\(\chi_{4815}(23, \cdot)\)	n/a	133952	208
4815.2.bv	\(\chi_{4815}(7, \cdot)\)	n/a	133952	208

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4815))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4815)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(107))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(321))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(535))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(963))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1605))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4815))\)\(^{\oplus 1}\)