Space of modular forms of level 5312 and weight 2

• Label: 5312.2
• Level: 5312
• Weight: 2
• Dimension: 494010
• Nonzero newspaces: 16
• Sturm bound: 3526656

Defining parameters

Level:	\( N \)	=	\( 5312 = 2^{6} \cdot 83 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(3526656\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5312))\).

	Total	New	Old
Modular forms	887568	497574	389994
Cusp forms	875761	494010	381751
Eisenstein series	11807	3564	8243

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5312))\)

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
5312.2.a	\(\chi_{5312}(1, \cdot)\)	5312.2.a.a	1	1
		5312.2.a.b	1
		5312.2.a.c	1
		5312.2.a.d	1
		5312.2.a.e	1
		5312.2.a.f	1
		5312.2.a.g	1
		5312.2.a.h	1
		5312.2.a.i	1
		5312.2.a.j	1
		5312.2.a.k	1
		5312.2.a.l	1
		5312.2.a.m	1
		5312.2.a.n	1
		5312.2.a.o	1
		5312.2.a.p	1
		5312.2.a.q	2
		5312.2.a.r	2
		5312.2.a.s	2
		5312.2.a.t	2
		5312.2.a.u	2
		5312.2.a.v	2
		5312.2.a.w	2
		5312.2.a.x	2
		5312.2.a.y	3
		5312.2.a.z	3
		5312.2.a.ba	3
		5312.2.a.bb	3
		5312.2.a.bc	3
		5312.2.a.bd	3
		5312.2.a.be	4
		5312.2.a.bf	4
		5312.2.a.bg	4
		5312.2.a.bh	4
		5312.2.a.bi	5
		5312.2.a.bj	5
		5312.2.a.bk	5
		5312.2.a.bl	5
		5312.2.a.bm	6
		5312.2.a.bn	6
		5312.2.a.bo	6
		5312.2.a.bp	6
		5312.2.a.bq	8
		5312.2.a.br	8
		5312.2.a.bs	8
		5312.2.a.bt	8
		5312.2.a.bu	11
		5312.2.a.bv	11
5312.2.b	\(\chi_{5312}(5311, \cdot)\)	n/a	166	1
5312.2.c	\(\chi_{5312}(2657, \cdot)\)	n/a	164	1
5312.2.h	\(\chi_{5312}(2655, \cdot)\)	n/a	168	1
5312.2.j	\(\chi_{5312}(1329, \cdot)\)	n/a	328	2
5312.2.l	\(\chi_{5312}(1327, \cdot)\)	n/a	332	2
5312.2.m	\(\chi_{5312}(663, \cdot)\)	None	0	4
5312.2.n	\(\chi_{5312}(665, \cdot)\)	None	0	4
5312.2.q	\(\chi_{5312}(333, \cdot)\)	n/a	5248	8
5312.2.t	\(\chi_{5312}(331, \cdot)\)	n/a	5360	8
5312.2.u	\(\chi_{5312}(65, \cdot)\)	n/a	6640	40
5312.2.v	\(\chi_{5312}(159, \cdot)\)	n/a	6720	40
5312.2.ba	\(\chi_{5312}(33, \cdot)\)	n/a	6720	40
5312.2.bb	\(\chi_{5312}(255, \cdot)\)	n/a	6640	40
5312.2.bc	\(\chi_{5312}(15, \cdot)\)	n/a	13280	80
5312.2.be	\(\chi_{5312}(17, \cdot)\)	n/a	13280	80
5312.2.bi	\(\chi_{5312}(9, \cdot)\)	None	0	160
5312.2.bj	\(\chi_{5312}(39, \cdot)\)	None	0	160
5312.2.bk	\(\chi_{5312}(19, \cdot)\)	n/a	214400	320
5312.2.bn	\(\chi_{5312}(21, \cdot)\)	n/a	214400	320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5312))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(166))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(332))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(664))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2656))\)\(^{\oplus 2}\)