Space of modular forms of level 25 and weight 2

• Label: 25.2
• Level: 25
• Weight: 2
• Dimension: 12
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 100
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(100\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	39	33	6
Cusp forms	12	12	0
Eisenstein series	27	21	6

Trace form

12 * q - 7 * q^2 - 6 * q^3 - 3 * q^4 - 5 * q^5 - 6 * q^6 - 2 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 - 6 * q^11 + 18 * q^12 + 4 * q^13 + 14 * q^14 + 10 * q^15 - 3 * q^16 - 2 * q^17 + 4 * q^18 - 10 * q^19 - 10 * q^20 - 6 * q^21 - 14 * q^22 - 6 * q^23 - 20 * q^24 - 15 * q^25 - 6 * q^26 - 14 * q^28 + 10 * q^30 - 6 * q^31 + 18 * q^32 + 18 * q^33 + 19 * q^34 + 20 * q^35 + 17 * q^36 + 23 * q^37 + 20 * q^38 + 6 * q^39 + 15 * q^40 + 4 * q^41 - 14 * q^42 - 6 * q^43 + 4 * q^44 - 25 * q^45 - 6 * q^46 - 2 * q^47 - 36 * q^48 - 8 * q^49 - 25 * q^50 - 16 * q^51 - 22 * q^52 - q^53 - 20 * q^54 + 10 * q^55 + 10 * q^56 - 10 * q^57 + 10 * q^58 - 10 * q^60 + 4 * q^61 - 24 * q^62 + 4 * q^63 + 7 * q^64 + 5 * q^65 + 18 * q^66 + 18 * q^67 - 4 * q^68 + 16 * q^69 + 30 * q^70 + 14 * q^71 + 15 * q^72 + 24 * q^73 - 6 * q^74 + 10 * q^75 + 6 * q^77 + 28 * q^78 + 30 * q^79 + 5 * q^80 + 27 * q^81 - 4 * q^82 - 36 * q^83 + 14 * q^84 - 35 * q^85 - 6 * q^86 - 20 * q^87 - 30 * q^88 - 45 * q^89 - 25 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 - 26 * q^94 + 10 * q^95 + 14 * q^96 - 52 * q^97 + q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.2.a	\(\chi_{25}(1, \cdot)\)	None	0	1
25.2.b	\(\chi_{25}(24, \cdot)\)	None	0	1
25.2.d	\(\chi_{25}(6, \cdot)\)	25.2.d.a	4	4
25.2.e	\(\chi_{25}(4, \cdot)\)	25.2.e.a	8	4