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Properties

Label 25.38
Level 25
Weight 38
Dimension 843
Nonzero newspaces 4
Sturm bound 1900
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 38 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1900\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_1(25))\).

Total New Old
Modular forms 939 864 75
Cusp forms 911 843 68
Eisenstein series 28 21 7

Trace form

\( 843 q - 718694 q^{2} - 244505402 q^{3} + 450037130238 q^{4} - 12148608761885 q^{5} - 149127661216754 q^{6} - 13822765238097194 q^{7} + 68198119842612710 q^{8} + 1286931875247529962 q^{9} + O(q^{10}) \) \( 843 q - 718694 q^{2} - 244505402 q^{3} + 450037130238 q^{4} - 12148608761885 q^{5} - 149127661216754 q^{6} - 13822765238097194 q^{7} + 68198119842612710 q^{8} + 1286931875247529962 q^{9} + 10552133327503169840 q^{10} - 7061429557216418914 q^{11} - 372546921181103572074 q^{12} - 117545670484846405082 q^{13} + 5017017250407421066886 q^{14} + 7207302325355285986890 q^{15} - 477137135315382954912882 q^{16} - 331404132260050626632404 q^{17} + 857428853636683284323338 q^{18} + 2456298400934470982794610 q^{19} - 1729136305594933622828470 q^{20} - 1323121478109511838466054 q^{21} + 79407043119464883833699302 q^{22} + 31134323253641664396012418 q^{23} + 9313013373173444917704940 q^{24} + 159725133351250512824753085 q^{25} - 551515255335671318094959364 q^{26} + 1176025032371051840643743080 q^{27} - 2625268313991293896073337098 q^{28} + 10044812394099968756266995530 q^{29} + 4390619241118759962717241750 q^{30} - 426615393894908566927853574 q^{31} + 51744139169076008353140175286 q^{32} - 7950238531815820708036605054 q^{33} - 159660462959202610518447604994 q^{34} + 14644835622758168600719654980 q^{35} - 1084599402222985171390857605322 q^{36} + 149746963041049013700366511001 q^{37} + 2323166113539813011825410174540 q^{38} + 255270667231789748486813761614 q^{39} + 2641588125051067970958137756940 q^{40} + 275375299932157006000465922466 q^{41} + 15363818656581070955511920454202 q^{42} - 5869232441307722823561922046562 q^{43} + 35865405322953778911661587471976 q^{44} - 19805148362163450208851734606965 q^{45} + 3908183690161959914238239350506 q^{46} - 47176926280365135560107786976434 q^{47} + 44387211315852895602605762867988 q^{48} - 81159872704820550689212235123837 q^{49} + 236599207479828859420796378083650 q^{50} - 37292800041904482773487283495464 q^{51} - 59523750133810306969149806886844 q^{52} - 37773998653735692285108862387247 q^{53} - 728533669438165642141446316070800 q^{54} + 521799435915226978619569857276250 q^{55} - 842005875053923784592196177682990 q^{56} + 1529256701784509292029149271747750 q^{57} - 3598204506615853976566278962314460 q^{58} + 4139088216911759553188318831475460 q^{59} + 4376894747919519611605293969276050 q^{60} + 2457533812357102920259110507002206 q^{61} + 3836190380496306059561800728560272 q^{62} - 4543820264435917837110259464674452 q^{63} + 24636913088849699434253558205726808 q^{64} + 26188350554028328776301590787872385 q^{65} - 31039834593247908190896427796540818 q^{66} + 40750932847610671635420641124788766 q^{67} - 106263887469374827413618544574247258 q^{68} + 43924007511933578314939244289839824 q^{69} + 54152942623228557036327252129616110 q^{70} - 2185813681653500511725156172425754 q^{71} + 223087856457533324618918111214419880 q^{72} + 105889925997139606959414378773843598 q^{73} - 435806490231133918773168089237129564 q^{74} + 241820538488657334953716344379442410 q^{75} + 294736941431620044646793675240504580 q^{76} - 940576348574544571700770043953839738 q^{77} + 904468875871232473201243639966960856 q^{78} + 161814168134734840904604428942812110 q^{79} - 2024748560406476471601996056604025850 q^{80} - 1916691868383119763032182150110028002 q^{81} - 1258824963794437445154966376178621818 q^{82} + 55321131887666404017871195025857448 q^{83} - 979739191232673264925467385621905754 q^{84} - 3149473581084146725804433626958111675 q^{85} + 4187524366100752479791081003006324666 q^{86} - 5945756116411242747162660809907613180 q^{87} + 7733233112033243153836260590425989630 q^{88} + 4129179637654166693117463461102632245 q^{89} - 28926937359942525006665683568331527970 q^{90} + 7998627447512573640932822531468318826 q^{91} - 16793683958762723259604643602153731934 q^{92} - 16923664054744427141954523911569161644 q^{93} + 38251318622685538360732177839413497606 q^{94} - 3839967208061552383838232665958329190 q^{95} - 3080804166749704658194389120206122294 q^{96} + 65199205653258007315296496052158904666 q^{97} - 54284226561242126266297603549928235258 q^{98} + 10767191054324882230882761657462683844 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.38.a \(\chi_{25}(1, \cdot)\) 25.38.a.a 2 1
25.38.a.b 6
25.38.a.c 7
25.38.a.d 12
25.38.a.e 12
25.38.a.f 18
25.38.b \(\chi_{25}(24, \cdot)\) 25.38.b.a 4 1
25.38.b.b 12
25.38.b.c 14
25.38.b.d 24
25.38.d \(\chi_{25}(6, \cdot)\) n/a 364 4
25.38.e \(\chi_{25}(4, \cdot)\) n/a 368 4

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

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)