Space of modular forms of level 250 and weight 2

• Label: 250.2
• Level: 250
• Weight: 2
• Dimension: 576
• Nonzero newspaces: 6
• Newform subspaces: 16
• Sturm bound: 7500
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(7500\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(250))\).

	Total	New	Old
Modular forms	2055	576	1479
Cusp forms	1696	576	1120
Eisenstein series	359	0	359

Trace form

576 * q + q^2 + 4 * q^3 + q^4 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + 12 * q^11 + 4 * q^12 + 14 * q^13 + 8 * q^14 + q^16 - 22 * q^17 - 37 * q^18 - 60 * q^19 - 5 * q^20 - 48 * q^21 - 68 * q^22 - 56 * q^23 - 36 * q^24 - 60 * q^25 - 26 * q^26 - 80 * q^27 - 32 * q^28 - 50 * q^29 - 40 * q^30 - 48 * q^31 - 9 * q^32 - 32 * q^33 - 32 * q^34 - 20 * q^35 + 13 * q^36 + 28 * q^37 + 20 * q^38 - 24 * q^39 + 2 * q^41 + 32 * q^42 - 36 * q^43 + 12 * q^44 - 80 * q^45 + 24 * q^46 - 32 * q^47 + 4 * q^48 - 33 * q^49 - 48 * q^51 + 14 * q^52 - 36 * q^53 + 40 * q^54 - 40 * q^55 + 8 * q^56 - 80 * q^57 + 30 * q^58 - 60 * q^59 - 20 * q^60 - 58 * q^61 - 88 * q^62 - 176 * q^63 + q^64 - 105 * q^65 - 72 * q^66 - 92 * q^67 - 102 * q^68 - 184 * q^69 - 80 * q^70 - 88 * q^71 + 13 * q^72 - 86 * q^73 - 162 * q^74 - 160 * q^75 - 60 * q^76 - 224 * q^77 - 144 * q^78 - 80 * q^79 - 39 * q^81 - 118 * q^82 - 236 * q^83 - 88 * q^84 - 105 * q^85 - 76 * q^86 - 160 * q^87 + 12 * q^88 - 120 * q^89 - 60 * q^90 - 48 * q^91 - 16 * q^92 + 8 * q^93 + 48 * q^94 - 40 * q^95 + 4 * q^96 + 58 * q^97 + 57 * q^98 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)

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
250.2.a	\(\chi_{250}(1, \cdot)\)	250.2.a.a	2	1
		250.2.a.b	2
		250.2.a.c	2
		250.2.a.d	2
250.2.b	\(\chi_{250}(249, \cdot)\)	250.2.b.a	4	1
		250.2.b.b	4
250.2.d	\(\chi_{250}(51, \cdot)\)	250.2.d.a	4	4
		250.2.d.b	8
		250.2.d.c	8
		250.2.d.d	8
250.2.e	\(\chi_{250}(49, \cdot)\)	250.2.e.a	8	4
		250.2.e.b	8
		250.2.e.c	16
250.2.g	\(\chi_{250}(11, \cdot)\)	250.2.g.a	120	20
		250.2.g.b	140
250.2.h	\(\chi_{250}(9, \cdot)\)	250.2.h.a	240	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(250))\) into lower level spaces

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