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Properties

Label 22.20
Level 22
Weight 20
Dimension 91
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(22))\).

Total New Old
Modular forms 295 91 204
Cusp forms 275 91 184
Eisenstein series 20 0 20

Trace form

\( 91 q + 132240 q^{3} - 1048576 q^{4} - 1979640 q^{5} - 25939456 q^{6} - 320746110 q^{7} + 6534368192 q^{9} + O(q^{10}) \) \( 91 q + 132240 q^{3} - 1048576 q^{4} - 1979640 q^{5} - 25939456 q^{6} - 320746110 q^{7} + 6534368192 q^{9} + 2394168320 q^{10} + 4891126826 q^{11} - 5879889920 q^{12} + 31724462850 q^{13} + 212274025472 q^{14} - 883109580970 q^{15} - 274877906944 q^{16} + 1521554832280 q^{17} - 2189665016320 q^{18} + 2532971753215 q^{19} - 518950748160 q^{20} - 18073394746788 q^{21} + 2805257994240 q^{22} + 36764122868340 q^{23} - 6799872753664 q^{24} - 14196363743100 q^{25} - 40532428404736 q^{26} + 164546720539005 q^{27} - 81094275235840 q^{28} + 190011892344980 q^{29} + 175299698242560 q^{30} + 344061809080822 q^{31} - 175921860444160 q^{32} + 522999861710065 q^{33} + 1551082163382272 q^{34} - 2433935916149300 q^{35} - 875921862295552 q^{36} + 988837608742140 q^{37} + 7699859007144960 q^{38} - 9293904751691926 q^{39} + 191903165317120 q^{40} + 12158870499971972 q^{41} + 12306969117885440 q^{42} - 44640213358036790 q^{43} + 9745732707549184 q^{44} + 2966593632684230 q^{45} - 27599243597879296 q^{46} - 4551956848342240 q^{47} + 9087463603568640 q^{48} - 36551811605351012 q^{49} - 15071742831994880 q^{50} - 78342891330724943 q^{51} + 48645665650114560 q^{52} - 37930860871128190 q^{53} - 100838391591628800 q^{54} - 150717101608106410 q^{55} + 37895218007113728 q^{56} + 271923452367394695 q^{57} - 170603252905840640 q^{58} - 183341244863096095 q^{59} - 173680082524569600 q^{60} + 318185375444919702 q^{61} + 157247680646292480 q^{62} - 281742613228341560 q^{63} - 72057594037927936 q^{64} - 1431488077229464220 q^{65} - 410218646836975616 q^{66} + 514708616233407810 q^{67} + 398866469953208320 q^{68} + 2514523147383706974 q^{69} - 1430368658668451840 q^{70} - 3571291726716590928 q^{71} - 505135589239029760 q^{72} + 816761830767326560 q^{73} + 1532950278114936832 q^{74} - 2937146970487760645 q^{75} - 584944840424816640 q^{76} - 1905236694492436260 q^{77} + 116442640723701760 q^{78} + 8985156682922422410 q^{79} + 435047201735966720 q^{80} - 7068318491488340679 q^{81} - 6699731585738401280 q^{82} - 9150557827050807295 q^{83} + 6972653194191044608 q^{84} + 20561140583194249830 q^{85} + 3663021943357919744 q^{86} - 35139193302878229260 q^{87} - 2617145635341598720 q^{88} + 26179239357759385580 q^{89} + 34291425919489735680 q^{90} - 24087243043692574628 q^{91} - 13671944832063897600 q^{92} - 29714953232217890650 q^{93} + 20219799115577884672 q^{94} + 15067265796471308150 q^{95} + 2810246167479189504 q^{96} + 9216284138792440905 q^{97} - 29975884166995130880 q^{98} + 3232694193362220442 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.20.a \(\chi_{22}(1, \cdot)\) 22.20.a.a 1 1
22.20.a.b 2
22.20.a.c 4
22.20.a.d 4
22.20.a.e 4
22.20.c \(\chi_{22}(3, \cdot)\) 22.20.c.a 36 4
22.20.c.b 40

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)