Space of modular forms of level 25 and weight 8

• Label: 25.8
• Level: 25
• Weight: 8
• Dimension: 151
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 400
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(400\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	189	172	17
Cusp forms	161	151	10
Eisenstein series	28	21	7

Trace form

151 * q - 22 * q^2 + 46 * q^3 - 386 * q^4 - 35 * q^5 + 2062 * q^6 + 3478 * q^7 - 4570 * q^8 - 15924 * q^9 - 1560 * q^10 + 17862 * q^11 + 53238 * q^12 - 14814 * q^13 - 79162 * q^14 - 8910 * q^15 - 6514 * q^16 + 143008 * q^17 + 86626 * q^18 - 123910 * q^19 - 309670 * q^20 - 209478 * q^21 - 178554 * q^22 + 404466 * q^23 + 1367980 * q^24 + 446835 * q^25 - 147588 * q^26 - 895760 * q^27 - 1401386 * q^28 - 329850 * q^29 - 945050 * q^30 - 593078 * q^31 + 945078 * q^32 + 2054562 * q^33 + 2381798 * q^34 - 139420 * q^35 - 881994 * q^36 - 1384157 * q^37 - 901540 * q^38 + 1378782 * q^39 + 2620940 * q^40 + 687022 * q^41 - 2497094 * q^42 - 3363914 * q^43 - 8397752 * q^44 - 3473515 * q^45 + 4287242 * q^46 + 3184798 * q^47 + 8681556 * q^48 + 1278199 * q^49 + 8958650 * q^50 + 2972232 * q^51 + 4173348 * q^52 + 4777211 * q^53 - 11273920 * q^54 - 5520550 * q^55 - 13305710 * q^56 - 16620250 * q^57 - 11571980 * q^58 - 7671900 * q^59 + 18699650 * q^60 + 5584082 * q^61 + 30259776 * q^62 + 20269556 * q^63 + 5707544 * q^64 - 11933665 * q^65 - 16586866 * q^66 - 20731002 * q^67 - 23354266 * q^68 - 6482528 * q^69 - 5968290 * q^70 - 4975018 * q^71 + 33254520 * q^72 + 13693106 * q^73 + 28673508 * q^74 + 28907410 * q^75 + 25801540 * q^76 + 7556166 * q^77 - 15930808 * q^78 - 12899570 * q^79 - 48504250 * q^80 - 22088184 * q^81 - 64074234 * q^82 - 17217864 * q^83 + 11623718 * q^84 + 51064175 * q^85 + 41008122 * q^86 + 82366460 * q^87 + 21995070 * q^88 - 26015445 * q^89 - 60427770 * q^90 - 20358438 * q^91 - 115601502 * q^92 - 132708428 * q^93 - 57253882 * q^94 + 15736810 * q^95 + 35035562 * q^96 + 97782198 * q^97 + 201394774 * q^98 + 141831852 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.8.a	\(\chi_{25}(1, \cdot)\)	25.8.a.a	1	1
		25.8.a.b	2
		25.8.a.c	2
		25.8.a.d	2
		25.8.a.e	2
25.8.b	\(\chi_{25}(24, \cdot)\)	25.8.b.a	2	1
		25.8.b.b	4
		25.8.b.c	4
25.8.d	\(\chi_{25}(6, \cdot)\)	25.8.d.a	68	4
25.8.e	\(\chi_{25}(4, \cdot)\)	25.8.e.a	64	4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)