Space of modular forms of level 5194 and weight 2

• Label: 5194.2
• Level: 5194
• Weight: 2
• Dimension: 263879
• Nonzero newspaces: 24
• Sturm bound: 3302208

Defining parameters

Level:	\( N \)	=	\( 5194 = 2 \cdot 7^{2} \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(3302208\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5194))\).

	Total	New	Old
Modular forms	831792	263879	567913
Cusp forms	819313	263879	555434
Eisenstein series	12479	0	12479

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5194))\)

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
5194.2.a	\(\chi_{5194}(1, \cdot)\)	5194.2.a.a	1	1
		5194.2.a.b	1
		5194.2.a.c	1
		5194.2.a.d	1
		5194.2.a.e	1
		5194.2.a.f	1
		5194.2.a.g	1
		5194.2.a.h	1
		5194.2.a.i	1
		5194.2.a.j	1
		5194.2.a.k	1
		5194.2.a.l	1
		5194.2.a.m	1
		5194.2.a.n	1
		5194.2.a.o	1
		5194.2.a.p	1
		5194.2.a.q	1
		5194.2.a.r	2
		5194.2.a.s	2
		5194.2.a.t	2
		5194.2.a.u	2
		5194.2.a.v	2
		5194.2.a.w	2
		5194.2.a.x	2
		5194.2.a.y	2
		5194.2.a.z	2
		5194.2.a.ba	2
		5194.2.a.bb	2
		5194.2.a.bc	2
		5194.2.a.bd	3
		5194.2.a.be	3
		5194.2.a.bf	3
		5194.2.a.bg	3
		5194.2.a.bh	4
		5194.2.a.bi	4
		5194.2.a.bj	4
		5194.2.a.bk	4
		5194.2.a.bl	4
		5194.2.a.bm	4
		5194.2.a.bn	4
		5194.2.a.bo	4
		5194.2.a.bp	6
		5194.2.a.bq	6
		5194.2.a.br	6
		5194.2.a.bs	7
		5194.2.a.bt	7
		5194.2.a.bu	8
		5194.2.a.bv	8
		5194.2.a.bw	9
		5194.2.a.bx	9
		5194.2.a.by	10
		5194.2.a.bz	18
5194.2.c	\(\chi_{5194}(3921, \cdot)\)	n/a	184	1
5194.2.e	\(\chi_{5194}(2333, \cdot)\)	n/a	344	2
5194.2.f	\(\chi_{5194}(1567, \cdot)\)	n/a	360	2
5194.2.j	\(\chi_{5194}(1059, \cdot)\)	n/a	360	2
5194.2.k	\(\chi_{5194}(743, \cdot)\)	n/a	1440	6
5194.2.l	\(\chi_{5194}(129, \cdot)\)	n/a	720	4
5194.2.n	\(\chi_{5194}(99, \cdot)\)	n/a	2220	12
5194.2.p	\(\chi_{5194}(211, \cdot)\)	n/a	1512	6
5194.2.r	\(\chi_{5194}(107, \cdot)\)	n/a	2928	12
5194.2.t	\(\chi_{5194}(197, \cdot)\)	n/a	2208	12
5194.2.w	\(\chi_{5194}(83, \cdot)\)	n/a	3024	12
5194.2.x	\(\chi_{5194}(275, \cdot)\)	n/a	4320	24
5194.2.y	\(\chi_{5194}(317, \cdot)\)	n/a	3024	12
5194.2.bc	\(\chi_{5194}(391, \cdot)\)	n/a	4320	24
5194.2.bd	\(\chi_{5194}(165, \cdot)\)	n/a	4320	24
5194.2.bh	\(\chi_{5194}(341, \cdot)\)	n/a	6048	24
5194.2.bi	\(\chi_{5194}(15, \cdot)\)	n/a	18144	72
5194.2.bk	\(\chi_{5194}(19, \cdot)\)	n/a	8640	48
5194.2.bm	\(\chi_{5194}(29, \cdot)\)	n/a	18144	72
5194.2.bo	\(\chi_{5194}(81, \cdot)\)	n/a	36288	144
5194.2.bp	\(\chi_{5194}(27, \cdot)\)	n/a	36288	144
5194.2.bt	\(\chi_{5194}(9, \cdot)\)	n/a	36288	144
5194.2.bu	\(\chi_{5194}(3, \cdot)\)	n/a	72576	288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5194))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5194)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(371))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(742))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2597))\)\(^{\oplus 2}\)