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Properties

Label 22.12
Level 22
Weight 12
Dimension 55
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(22))\).

Total New Old
Modular forms 175 55 120
Cusp forms 155 55 100
Eisenstein series 20 0 20

Trace form

\( 55 q + 31520 q^{6} - 191830 q^{7} + 320780 q^{9} + O(q^{10}) \) \( 55 q + 31520 q^{6} - 191830 q^{7} + 320780 q^{9} - 1000000 q^{10} + 152690 q^{11} + 2590720 q^{12} - 30130 q^{13} - 6343360 q^{14} + 8701910 q^{15} - 16483700 q^{17} - 15924640 q^{18} + 31594215 q^{19} - 81682020 q^{21} - 81447300 q^{23} + 32276480 q^{24} + 210335000 q^{25} - 236417920 q^{26} - 588235515 q^{27} + 80660480 q^{28} + 939532040 q^{29} + 321741120 q^{30} - 937824330 q^{31} - 167772160 q^{32} - 1359728315 q^{33} + 294574720 q^{34} + 2795206540 q^{35} + 265272320 q^{36} + 81140860 q^{37} - 2094682560 q^{38} - 1437759790 q^{39} - 418447360 q^{40} + 3395493680 q^{41} + 845756480 q^{42} - 920501510 q^{43} + 591600640 q^{44} + 4738694510 q^{45} - 4044241280 q^{46} - 5020677160 q^{47} + 9187574940 q^{49} + 6515547520 q^{50} + 8716699705 q^{51} - 310415360 q^{52} - 4229508970 q^{53} - 18366600960 q^{54} - 6012342970 q^{55} - 20733567825 q^{57} + 26561918720 q^{58} + 27849121145 q^{59} + 5588766720 q^{60} + 2978390210 q^{61} - 36774482880 q^{62} - 41718596360 q^{63} - 8954981540 q^{65} + 1821527680 q^{66} + 8158288050 q^{67} - 16879308800 q^{68} - 20285178870 q^{69} + 26634803840 q^{70} + 124690788720 q^{71} + 34472591360 q^{72} + 9782937180 q^{73} - 12741879680 q^{74} - 242936282045 q^{75} - 25355253760 q^{76} - 34792021800 q^{77} - 36851851520 q^{78} + 112299873010 q^{79} + 26539458560 q^{80} + 94540010205 q^{81} - 28349940320 q^{82} + 245320055705 q^{83} + 104887705600 q^{84} + 22355188570 q^{85} - 192092727520 q^{86} - 489839116700 q^{87} - 14994964480 q^{88} - 165366270520 q^{89} + 310227579840 q^{90} + 380087853740 q^{91} + 194998794240 q^{92} + 234935478710 q^{93} + 74627919360 q^{94} + 474980447150 q^{95} - 696874113995 q^{97} - 406764358560 q^{98} - 1133072922830 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.12.a \(\chi_{22}(1, \cdot)\) 22.12.a.a 2 1
22.12.a.b 3
22.12.a.c 3
22.12.a.d 3
22.12.c \(\chi_{22}(3, \cdot)\) 22.12.c.a 20 4
22.12.c.b 24

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)