Space of modular forms of level 4375 and weight 2

• Label: 4375.2
• Level: 4375
• Weight: 2
• Dimension: 658560
• Nonzero newspaces: 24
• Sturm bound: 3000000

Defining parameters

Level:	\( N \)	=	\( 4375 = 5^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(3000000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4375))\).

	Total	New	Old
Modular forms	756600	666240	90360
Cusp forms	743401	658560	84841
Eisenstein series	13199	7680	5519

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4375))\)

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
4375.2.a	\(\chi_{4375}(1, \cdot)\)	4375.2.a.a	2	1
		4375.2.a.b	2
		4375.2.a.c	8
		4375.2.a.d	8
		4375.2.a.e	12
		4375.2.a.f	12
		4375.2.a.g	14
		4375.2.a.h	14
		4375.2.a.i	16
		4375.2.a.j	16
		4375.2.a.k	16
		4375.2.a.l	16
		4375.2.a.m	24
		4375.2.a.n	24
		4375.2.a.o	28
		4375.2.a.p	28
4375.2.b	\(\chi_{4375}(624, \cdot)\)	n/a	240	1
4375.2.e	\(\chi_{4375}(2501, \cdot)\)	n/a	608	2
4375.2.f	\(\chi_{4375}(1693, \cdot)\)	n/a	608	2
4375.2.h	\(\chi_{4375}(876, \cdot)\)	n/a	960	4
4375.2.k	\(\chi_{4375}(3124, \cdot)\)	n/a	608	2
4375.2.n	\(\chi_{4375}(1499, \cdot)\)	n/a	960	4
4375.2.o	\(\chi_{4375}(2943, \cdot)\)	n/a	1216	4
4375.2.q	\(\chi_{4375}(501, \cdot)\)	n/a	2464	8
4375.2.s	\(\chi_{4375}(307, \cdot)\)	n/a	2464	8
4375.2.t	\(\chi_{4375}(176, \cdot)\)	n/a	4480	20
4375.2.u	\(\chi_{4375}(249, \cdot)\)	n/a	2464	8
4375.2.y	\(\chi_{4375}(99, \cdot)\)	n/a	4520	20
4375.2.bb	\(\chi_{4375}(68, \cdot)\)	n/a	4928	16
4375.2.bc	\(\chi_{4375}(51, \cdot)\)	n/a	11760	40
4375.2.bd	\(\chi_{4375}(118, \cdot)\)	n/a	11760	40
4375.2.bf	\(\chi_{4375}(36, \cdot)\)	n/a	37600	100
4375.2.bh	\(\chi_{4375}(74, \cdot)\)	n/a	11760	40
4375.2.bl	\(\chi_{4375}(29, \cdot)\)	n/a	37400	100
4375.2.bn	\(\chi_{4375}(82, \cdot)\)	n/a	23520	80
4375.2.bo	\(\chi_{4375}(11, \cdot)\)	n/a	99600	200
4375.2.bp	\(\chi_{4375}(13, \cdot)\)	n/a	99600	200
4375.2.bs	\(\chi_{4375}(4, \cdot)\)	n/a	99600	200
4375.2.bv	\(\chi_{4375}(3, \cdot)\)	n/a	199200	400

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4375))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4375)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(875))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4375))\)\(^{\oplus 1}\)