Space of modular forms of level 25 and weight 4

• Label: 25.4
• Level: 25
• Weight: 4
• Dimension: 59
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 200
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(200\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	89	80	9
Cusp forms	61	59	2
Eisenstein series	28	21	7

Trace form

59 * q - 2 * q^2 - 14 * q^3 - 26 * q^4 - 5 * q^5 - 2 * q^6 - 22 * q^7 - 10 * q^8 + 36 * q^9 - 30 * q^10 - 82 * q^11 - 42 * q^12 + 66 * q^13 + 38 * q^14 - 146 * q^16 - 382 * q^17 - 644 * q^18 - 330 * q^19 + 170 * q^20 + 198 * q^21 + 966 * q^22 + 586 * q^23 + 1420 * q^24 + 685 * q^25 + 108 * q^26 + 730 * q^27 + 614 * q^28 + 170 * q^29 - 290 * q^30 - 162 * q^31 - 1642 * q^32 - 1098 * q^33 - 1452 * q^34 - 840 * q^35 - 1026 * q^36 - 1077 * q^37 - 1700 * q^38 - 2298 * q^39 - 2060 * q^40 - 522 * q^41 - 614 * q^42 - 614 * q^43 + 808 * q^44 + 2195 * q^45 + 1578 * q^46 + 2738 * q^47 + 6276 * q^48 + 2799 * q^49 + 4500 * q^50 + 2688 * q^51 + 4388 * q^52 + 1651 * q^53 + 2960 * q^54 + 910 * q^55 - 110 * q^56 - 970 * q^57 - 2020 * q^58 - 4310 * q^59 - 11470 * q^60 - 2802 * q^61 - 11144 * q^62 - 7954 * q^63 - 6696 * q^64 - 1955 * q^65 - 1114 * q^66 + 458 * q^67 + 3414 * q^68 + 3382 * q^69 + 4190 * q^70 + 1638 * q^71 + 9240 * q^72 + 4626 * q^73 + 9508 * q^74 + 5860 * q^75 + 3620 * q^76 + 5046 * q^77 + 5312 * q^78 + 950 * q^79 + 5830 * q^80 - 2496 * q^81 - 6674 * q^82 - 7354 * q^83 - 13402 * q^84 - 9645 * q^85 - 4942 * q^86 - 8470 * q^87 - 12610 * q^88 - 7335 * q^89 - 8160 * q^90 - 1362 * q^91 - 3742 * q^92 + 4582 * q^93 + 6918 * q^94 + 6810 * q^95 + 4778 * q^96 + 12238 * q^97 + 11034 * q^98 + 13332 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.4.a	\(\chi_{25}(1, \cdot)\)	25.4.a.a	1	1
		25.4.a.b	1
		25.4.a.c	1
25.4.b	\(\chi_{25}(24, \cdot)\)	25.4.b.a	2	1
		25.4.b.b	2
25.4.d	\(\chi_{25}(6, \cdot)\)	25.4.d.a	28	4
25.4.e	\(\chi_{25}(4, \cdot)\)	25.4.e.a	24	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)