Space of modular forms of level 3750 and weight 2

• Label: 3750.2
• Level: 3750
• Weight: 2
• Dimension: 86400
• Nonzero newspaces: 12
• Sturm bound: 1500000
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(1500000\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3750))\).

	Total	New	Old
Modular forms	379400	86400	293000
Cusp forms	370601	86400	284201
Eisenstein series	8799	0	8799

Trace form

86400 * q - 40 * q^17 - 10 * q^18 - 80 * q^19 - 40 * q^21 - 80 * q^22 - 80 * q^23 - 20 * q^24 - 40 * q^26 - 40 * q^28 - 80 * q^29 - 80 * q^31 - 10 * q^32 - 40 * q^33 - 50 * q^34 - 10 * q^37 - 40 * q^39 - 40 * q^41 - 80 * q^43 - 80 * q^47 - 90 * q^49 - 60 * q^51 - 90 * q^53 - 80 * q^57 - 80 * q^59 - 40 * q^61 + 60 * q^63 + 60 * q^66 + 140 * q^69 + 100 * q^78 + 80 * q^81 - 40 * q^83 + 60 * q^84 + 60 * q^87 - 10 * q^89 - 80 * q^91 - 20 * q^93 - 40 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3750))\)

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
3750.2.a	\(\chi_{3750}(1, \cdot)\)	3750.2.a.a	2	1
		3750.2.a.b	2
		3750.2.a.c	2
		3750.2.a.d	2
		3750.2.a.e	2
		3750.2.a.f	2
		3750.2.a.g	2
		3750.2.a.h	2
		3750.2.a.i	4
		3750.2.a.j	4
		3750.2.a.k	4
		3750.2.a.l	4
		3750.2.a.m	4
		3750.2.a.n	4
		3750.2.a.o	4
		3750.2.a.p	4
		3750.2.a.q	4
		3750.2.a.r	4
		3750.2.a.s	4
		3750.2.a.t	4
		3750.2.a.u	8
		3750.2.a.v	8
3750.2.c	\(\chi_{3750}(1249, \cdot)\)	3750.2.c.a	4	1
		3750.2.c.b	4
		3750.2.c.c	4
		3750.2.c.d	4
		3750.2.c.e	8
		3750.2.c.f	8
		3750.2.c.g	8
		3750.2.c.h	8
		3750.2.c.i	8
		3750.2.c.j	8
		3750.2.c.k	16
3750.2.e	\(\chi_{3750}(443, \cdot)\)	n/a	320	2
3750.2.g	\(\chi_{3750}(751, \cdot)\)	n/a	320	4
3750.2.h	\(\chi_{3750}(499, \cdot)\)	n/a	320	4
3750.2.l	\(\chi_{3750}(557, \cdot)\)	n/a	1280	8
3750.2.m	\(\chi_{3750}(151, \cdot)\)	n/a	1520	20
3750.2.o	\(\chi_{3750}(49, \cdot)\)	n/a	1480	20
3750.2.r	\(\chi_{3750}(107, \cdot)\)	n/a	6000	40
3750.2.s	\(\chi_{3750}(31, \cdot)\)	n/a	12400	100
3750.2.u	\(\chi_{3750}(19, \cdot)\)	n/a	12600	100
3750.2.x	\(\chi_{3750}(17, \cdot)\)	n/a	50000	200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3750))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3750)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(750))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1875))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3750))\)\(^{\oplus 1}\)