Space of modular forms of level 25 and weight 3

• Label: 25.3
• Level: 25
• Weight: 3
• Dimension: 36
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 150
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(150\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	64	56	8
Cusp forms	36	36	0
Eisenstein series	28	20	8

Trace form

36 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 18 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 18 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 46 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 + 42 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 - 68 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 158 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 34 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 + 142 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 + 162 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 148 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 310 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 2 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 174 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 + 102 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 60 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 26 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 + 42 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 + 282 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 282 * q^96 + 270 * q^97 + 170 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)

We only show spaces with odd 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
25.3.c	\(\chi_{25}(7, \cdot)\)	25.3.c.a	4	2
25.3.f	\(\chi_{25}(2, \cdot)\)	25.3.f.a	32	8