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Properties

Label 5.22
Level 5
Weight 22
Dimension 17
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 44
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(44\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(5))\).

Total New Old
Modular forms 23 19 4
Cusp forms 19 17 2
Eisenstein series 4 2 2

Trace form

\( 17 q + 1598 q^{2} + 135434 q^{3} + 882684 q^{4} - 15410345 q^{5} + 55899184 q^{6} + 1197030358 q^{7} + 6286638600 q^{8} - 23058391379 q^{9} + O(q^{10}) \) \( 17 q + 1598 q^{2} + 135434 q^{3} + 882684 q^{4} - 15410345 q^{5} + 55899184 q^{6} + 1197030358 q^{7} + 6286638600 q^{8} - 23058391379 q^{9} + 83700465030 q^{10} + 187542039704 q^{11} - 503308196432 q^{12} + 57357098574 q^{13} + 1638980480568 q^{14} + 332102329310 q^{15} + 11925559499312 q^{16} + 733529966678 q^{17} + 81647171463494 q^{18} - 91056765702340 q^{19} + 290250943927340 q^{20} - 239584045218996 q^{21} - 203004688093624 q^{22} + 388545505306914 q^{23} - 985800842997120 q^{24} + 900632348044025 q^{25} - 1015000904289196 q^{26} - 1611730473858100 q^{27} - 247898758582784 q^{28} - 402707489681210 q^{29} - 4371411504177440 q^{30} + 3840982722433044 q^{31} + 6022308475794208 q^{32} - 47425047428324192 q^{33} + 95489734126728348 q^{34} - 41225445683987070 q^{35} + 70856287201943132 q^{36} + 26872991516371118 q^{37} + 38176781255684600 q^{38} - 197738467425060028 q^{39} + 187415398125207400 q^{40} - 21900825691548386 q^{41} - 334487502048658944 q^{42} + 395111109322505394 q^{43} - 1114504556208345392 q^{44} + 21869220540789835 q^{45} + 244062989952251224 q^{46} + 47044210186534238 q^{47} + 192063027362083264 q^{48} + 384541096588670729 q^{49} - 178216117902672850 q^{50} + 2224974175455330244 q^{51} + 1711589438388353048 q^{52} - 2532372504975675466 q^{53} - 2469366484103927840 q^{54} - 3717891504225835640 q^{55} + 13106605528137915360 q^{56} + 6067235229019091000 q^{57} - 14098088367269025500 q^{58} + 11337963937621493180 q^{59} - 18823871926947270320 q^{60} - 4820501580839547046 q^{61} + 28533087758085932736 q^{62} + 8967507041593209174 q^{63} - 91792096204982936896 q^{64} + 3809792616803364610 q^{65} + 75750561651661846208 q^{66} + 10473435607038416278 q^{67} + 9049459099955001256 q^{68} - 200004431795085113868 q^{69} - 23742020811717907320 q^{70} + 157958942504799056524 q^{71} + 273453111111150138600 q^{72} - 34103167714234877586 q^{73} - 135912572139744554492 q^{74} - 343082157926115086950 q^{75} + 595126056351120260720 q^{76} + 392698243802630342496 q^{77} - 452912683312301552432 q^{78} - 516474429376094465160 q^{79} - 609864257668382651920 q^{80} + 1155203051666162841637 q^{81} + 787498996898908950316 q^{82} - 324246264182686907646 q^{83} - 2429035400555749240992 q^{84} - 543548331532542261270 q^{85} + 2133774008524336907264 q^{86} + 1011767514843797750300 q^{87} - 624045884838102832800 q^{88} - 1714134103446650010630 q^{89} - 1288359891748515176290 q^{90} + 2476359100164489740924 q^{91} + 3458344050732703820928 q^{92} - 430585694785886094312 q^{93} - 6287987862100659845112 q^{94} + 12802854604361952100 q^{95} + 7316800234269421604864 q^{96} + 1183125700288881568238 q^{97} - 1026968381183437208114 q^{98} - 5108492076099840495448 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.22.a \(\chi_{5}(1, \cdot)\) 5.22.a.a 3 1
5.22.a.b 4
5.22.b \(\chi_{5}(4, \cdot)\) 5.22.b.a 10 1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)