Space of modular forms of level 25 and weight 12

• Label: 25.12
• Level: 25
• Weight: 12
• Dimension: 244
• Nonzero newspaces: 4
• Newform subspaces: 12
• Sturm bound: 600
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(600\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	289	265	24
Cusp forms	261	244	17
Eisenstein series	28	21	7

Trace form

244 * q + 34 * q^2 + 1258 * q^3 - 7618 * q^4 - 1415 * q^5 - 44882 * q^6 - 30466 * q^7 + 438950 * q^8 - 568527 * q^9 - 144240 * q^10 + 1222778 * q^11 + 3553974 * q^12 - 4347232 * q^13 - 4842106 * q^14 - 2862870 * q^15 - 8936306 * q^16 + 29725214 * q^17 - 60933422 * q^18 - 17995770 * q^19 + 43594490 * q^20 + 64484898 * q^21 + 99092838 * q^22 - 55902182 * q^23 - 137638100 * q^24 + 18953435 * q^25 + 660360108 * q^26 + 257578120 * q^27 - 916595818 * q^28 - 884576140 * q^29 + 1068201190 * q^30 + 965288218 * q^31 + 367763894 * q^32 - 1381664454 * q^33 - 932970386 * q^34 + 1128568500 * q^35 - 441712266 * q^36 - 958288751 * q^37 + 3668070940 * q^38 - 3170790714 * q^39 - 6084041460 * q^40 - 599362152 * q^41 + 11419102138 * q^42 + 5565759978 * q^43 - 433725176 * q^44 - 13347804475 * q^45 - 15782560502 * q^46 - 8870711746 * q^47 + 32782948308 * q^48 + 28825156592 * q^49 + 22775585250 * q^50 - 22132214352 * q^51 - 52339315356 * q^52 - 15707480327 * q^53 - 8839619680 * q^54 + 1839646890 * q^55 + 10311611410 * q^56 + 38089528310 * q^57 + 34354072740 * q^58 - 27700786280 * q^59 - 18168102430 * q^60 - 22701755712 * q^61 - 67780667072 * q^62 + 43913611508 * q^63 + 94275225752 * q^64 + 33654296575 * q^65 + 91768937006 * q^66 + 16178813154 * q^67 - 136300473498 * q^68 - 231754819244 * q^69 - 159101155970 * q^70 + 42936087918 * q^71 + 228628676760 * q^72 + 102235283508 * q^73 + 102108050644 * q^74 + 162324468610 * q^75 + 216551970500 * q^76 + 10972815558 * q^77 - 491067122104 * q^78 - 343741239010 * q^79 - 449220143930 * q^80 - 117706619511 * q^81 + 549639959798 * q^82 + 551826704708 * q^83 + 534303246374 * q^84 - 253126682705 * q^85 - 55885647622 * q^86 - 171874815700 * q^87 - 52228961090 * q^88 - 130080479715 * q^89 + 556875105870 * q^90 - 55525313462 * q^91 - 268399844446 * q^92 - 567468984224 * q^93 - 434540657786 * q^94 - 177627752790 * q^95 - 551534348182 * q^96 + 55937607904 * q^97 + 807270722382 * q^98 + 1268950413456 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.12.a	\(\chi_{25}(1, \cdot)\)	25.12.a.a	1	1
		25.12.a.b	1
		25.12.a.c	2
		25.12.a.d	4
		25.12.a.e	4
		25.12.a.f	4
25.12.b	\(\chi_{25}(24, \cdot)\)	25.12.b.a	2	1
		25.12.b.b	2
		25.12.b.c	4
		25.12.b.d	8
25.12.d	\(\chi_{25}(6, \cdot)\)	25.12.d.a	108	4
25.12.e	\(\chi_{25}(4, \cdot)\)	25.12.e.a	104	4

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)