Space of modular forms of level 1250 and weight 2

• Label: 1250.2
• Level: 1250
• Weight: 2
• Dimension: 14400
• Nonzero newspaces: 8
• Sturm bound: 187500
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(187500\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1250))\).

	Total	New	Old
Modular forms	47975	14400	33575
Cusp forms	45776	14400	31376
Eisenstein series	2199	0	2199

Trace form

14400 * q + 20 * q^17 + 25 * q^18 + 40 * q^19 + 40 * q^21 + 40 * q^22 + 40 * q^23 + 20 * q^24 + 20 * q^26 + 60 * q^27 + 20 * q^28 + 40 * q^29 + 40 * q^31 + 5 * q^32 + 40 * q^33 + 25 * q^34 + 5 * q^37 + 40 * q^39 + 20 * q^41 + 40 * q^43 + 40 * q^47 + 45 * q^49 + 60 * q^51 + 45 * q^53 + 80 * q^57 + 60 * q^59 + 60 * q^61 + 60 * q^62 + 140 * q^63 + 60 * q^66 + 80 * q^67 + 60 * q^68 + 140 * q^69 + 80 * q^71 + 80 * q^73 + 100 * q^74 + 40 * q^76 + 160 * q^77 + 100 * q^78 + 80 * q^79 + 80 * q^81 + 80 * q^82 + 160 * q^83 + 60 * q^84 + 60 * q^86 + 140 * q^87 + 105 * q^89 + 80 * q^91 + 20 * q^92 + 60 * q^93 + 20 * q^97 + 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1250))\)

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
1250.2.a	\(\chi_{1250}(1, \cdot)\)	1250.2.a.a	2	1
		1250.2.a.b	2
		1250.2.a.c	2
		1250.2.a.d	2
		1250.2.a.e	4
		1250.2.a.f	4
		1250.2.a.g	4
		1250.2.a.h	4
		1250.2.a.i	4
		1250.2.a.j	4
		1250.2.a.k	4
		1250.2.a.l	4
1250.2.b	\(\chi_{1250}(1249, \cdot)\)	1250.2.b.a	4	1
		1250.2.b.b	4
		1250.2.b.c	8
		1250.2.b.d	8
		1250.2.b.e	8
		1250.2.b.f	8
1250.2.d	\(\chi_{1250}(251, \cdot)\)	n/a	160	4
1250.2.e	\(\chi_{1250}(249, \cdot)\)	n/a	160	4
1250.2.g	\(\chi_{1250}(51, \cdot)\)	n/a	740	20
1250.2.h	\(\chi_{1250}(49, \cdot)\)	n/a	760	20
1250.2.j	\(\chi_{1250}(11, \cdot)\)	n/a	6300	100
1250.2.k	\(\chi_{1250}(9, \cdot)\)	n/a	6200	100

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1250))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1250)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 2}\)