Space of modular forms of level 5290 and weight 2

• Label: 5290.2
• Level: 5290
• Weight: 2
• Dimension: 255067
• Nonzero newspaces: 12
• Sturm bound: 3351744

Defining parameters

Level:	\( N \)	=	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(3351744\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5290))\).

	Total	New	Old
Modular forms	843920	255067	588853
Cusp forms	831953	255067	576886
Eisenstein series	11967	0	11967

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5290))\)

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
5290.2.a	\(\chi_{5290}(1, \cdot)\)	5290.2.a.a	1	1
		5290.2.a.b	1
		5290.2.a.c	1
		5290.2.a.d	1
		5290.2.a.e	2
		5290.2.a.f	2
		5290.2.a.g	2
		5290.2.a.h	2
		5290.2.a.i	2
		5290.2.a.j	2
		5290.2.a.k	2
		5290.2.a.l	2
		5290.2.a.m	2
		5290.2.a.n	2
		5290.2.a.o	2
		5290.2.a.p	3
		5290.2.a.q	3
		5290.2.a.r	3
		5290.2.a.s	4
		5290.2.a.t	4
		5290.2.a.u	4
		5290.2.a.v	4
		5290.2.a.w	4
		5290.2.a.x	4
		5290.2.a.y	4
		5290.2.a.z	4
		5290.2.a.ba	4
		5290.2.a.bb	4
		5290.2.a.bc	5
		5290.2.a.bd	5
		5290.2.a.be	6
		5290.2.a.bf	6
		5290.2.a.bg	10
		5290.2.a.bh	10
		5290.2.a.bi	10
		5290.2.a.bj	10
		5290.2.a.bk	15
		5290.2.a.bl	15
5290.2.b	\(\chi_{5290}(1059, \cdot)\)	n/a	252	1
5290.2.e	\(\chi_{5290}(1057, \cdot)\)	n/a	504	2
5290.2.g	\(\chi_{5290}(501, \cdot)\)	n/a	1680	10
5290.2.j	\(\chi_{5290}(399, \cdot)\)	n/a	2520	10
5290.2.k	\(\chi_{5290}(231, \cdot)\)	n/a	4048	22
5290.2.m	\(\chi_{5290}(63, \cdot)\)	n/a	5040	20
5290.2.p	\(\chi_{5290}(139, \cdot)\)	n/a	6072	22
5290.2.r	\(\chi_{5290}(137, \cdot)\)	n/a	12144	44
5290.2.s	\(\chi_{5290}(31, \cdot)\)	n/a	40480	220
5290.2.t	\(\chi_{5290}(9, \cdot)\)	n/a	60720	220
5290.2.w	\(\chi_{5290}(7, \cdot)\)	n/a	121440	440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5290)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2645))\)\(^{\oplus 2}\)