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Properties

Label 25.24
Level 25
Weight 24
Dimension 521
Nonzero newspaces 4
Sturm bound 1200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(25))\).

Total New Old
Modular forms 589 542 47
Cusp forms 561 521 40
Eisenstein series 28 21 7

Trace form

\( 521 q - 3022 q^{2} - 326234 q^{3} + 160830 q^{4} - 149002655 q^{5} + 4403370862 q^{6} + 10964341078 q^{7} + 59233216550 q^{8} + 8186576070 q^{9} + O(q^{10}) \) \( 521 q - 3022 q^{2} - 326234 q^{3} + 160830 q^{4} - 149002655 q^{5} + 4403370862 q^{6} + 10964341078 q^{7} + 59233216550 q^{8} + 8186576070 q^{9} + 1507156366320 q^{10} - 364100698098 q^{11} - 195407516682 q^{12} + 22289327389726 q^{13} - 49745046541690 q^{14} - 31094514590550 q^{15} - 1034186230478194 q^{16} - 116750960448392 q^{17} + 1581385803589186 q^{18} - 1809417753760270 q^{19} + 585694319530970 q^{20} - 7024002008203038 q^{21} - 10616378248622874 q^{22} + 28231110987963426 q^{23} - 41978936746082900 q^{24} - 13732377836324065 q^{25} - 42286485683884788 q^{26} + 118708733754028720 q^{27} - 201098122385974826 q^{28} - 20276000788045590 q^{29} + 1091694672978507910 q^{30} - 519514263204320358 q^{31} + 995657725176077238 q^{32} - 475127794052050038 q^{33} + 1711758753766583470 q^{34} - 2845871037634955740 q^{35} - 4881874115942847114 q^{36} + 6039920584717513743 q^{37} + 1962295216597604540 q^{38} - 1505620467218582130 q^{39} + 11895474285115868940 q^{40} + 11580580667206889842 q^{41} + 72572401418502999226 q^{42} - 13340162042712158914 q^{43} - 91938431198636713400 q^{44} + 110893088259225016145 q^{45} - 24880108341153041078 q^{46} - 118298356793007222002 q^{47} + 102335089136661157716 q^{48} - 49497738556922539015 q^{49} + 136536126449642317250 q^{50} - 123918861752338968648 q^{51} - 25851736191222168412 q^{52} + 670068555574756729031 q^{53} - 244028968957726430080 q^{54} - 584339007661635360390 q^{55} + 221938222139260112530 q^{56} + 2054569737520488447110 q^{57} - 1654220363649423674460 q^{58} - 1336211016925375663380 q^{59} + 4786713042184345840130 q^{60} + 81510950236083980582 q^{61} + 304170343626032992416 q^{62} + 3108290998005705661916 q^{63} - 9662329180899313438440 q^{64} + 1339156595786869110995 q^{65} + 12242002997302313413934 q^{66} - 1829257474383884861602 q^{67} - 15072401759045090478106 q^{68} + 1894998678387758161780 q^{69} + 13331073029974515669790 q^{70} - 3802575280843568165818 q^{71} - 14389390299743157816840 q^{72} + 15269650357117136263766 q^{73} - 28513097414309967177420 q^{74} + 14065316792886350052610 q^{75} - 3336126065811290387900 q^{76} - 4637272208209646208954 q^{77} + 21083712889390817135912 q^{78} - 30049311814996063897010 q^{79} - 32295955551942370384570 q^{80} + 47192135558894713411866 q^{81} - 23927437214513117443114 q^{82} + 85835019181932288021216 q^{83} - 294935751541998274199770 q^{84} + 1117794771105743510455 q^{85} + 156465110557275070908282 q^{86} + 142080816308292519455300 q^{87} - 43839785024883633482690 q^{88} - 178330741131468571733565 q^{89} - 97537637029668970764210 q^{90} + 377572101997769806970042 q^{91} + 77976542311171836577698 q^{92} + 151575504000491691479392 q^{93} - 252709706435753646022010 q^{94} - 80793616308524831989190 q^{95} + 1237706341354834542016682 q^{96} + 139254039670945241733498 q^{97} + 57283412917448735057374 q^{98} - 988900273606708033759980 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.24.a \(\chi_{25}(1, \cdot)\) 25.24.a.a 2 1
25.24.a.b 3
25.24.a.c 4
25.24.a.d 8
25.24.a.e 8
25.24.a.f 10
25.24.b \(\chi_{25}(24, \cdot)\) 25.24.b.a 4 1
25.24.b.b 6
25.24.b.c 8
25.24.b.d 16
25.24.d \(\chi_{25}(6, \cdot)\) n/a 228 4
25.24.e \(\chi_{25}(4, \cdot)\) n/a 224 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)