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Properties

Label 22.11
Level 22
Weight 11
Dimension 50
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 330
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(330\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(22))\).

Total New Old
Modular forms 160 50 110
Cusp forms 140 50 90
Eisenstein series 20 0 20

Trace form

\( 50 q + 3520 q^{6} + 19470 q^{7} - 397100 q^{9} + O(q^{10}) \) \( 50 q + 3520 q^{6} + 19470 q^{7} - 397100 q^{9} + 490390 q^{11} + 158720 q^{12} - 1033230 q^{13} - 1020800 q^{14} + 1780240 q^{15} - 568590 q^{17} - 1696640 q^{18} - 6441270 q^{19} + 26566190 q^{23} + 1802240 q^{24} - 89668260 q^{25} - 401280 q^{26} + 83586360 q^{27} + 23541760 q^{28} + 12127610 q^{29} - 130637760 q^{30} - 196273880 q^{31} + 324393300 q^{33} + 156344960 q^{34} + 141198970 q^{35} - 13573120 q^{36} - 222194500 q^{37} - 411491520 q^{38} - 135488210 q^{39} + 111738880 q^{40} + 578410030 q^{41} + 722036480 q^{42} - 571125760 q^{44} - 30903120 q^{45} - 18444800 q^{46} + 995310250 q^{47} + 626604550 q^{49} - 249370880 q^{50} - 3189117030 q^{51} - 1047664640 q^{52} - 569689890 q^{53} + 48474760 q^{55} + 4693248230 q^{57} + 1663439360 q^{58} + 2196889200 q^{59} - 1614919680 q^{60} - 7196746370 q^{61} + 333819200 q^{62} - 5611880780 q^{63} + 1450611200 q^{66} + 10025523550 q^{67} - 291118080 q^{68} + 6316839650 q^{69} + 4403199680 q^{70} - 5539367240 q^{71} - 3240427520 q^{72} - 11932315010 q^{73} - 4772690560 q^{74} - 13494558330 q^{75} + 21848316350 q^{77} + 11929253120 q^{78} + 14374641710 q^{79} + 2912419840 q^{80} - 119274430 q^{81} + 10910190720 q^{82} + 9397002450 q^{83} - 19414517760 q^{84} - 62914747830 q^{85} - 25960809600 q^{86} + 4467425280 q^{88} + 53554381570 q^{89} + 65417397760 q^{90} + 40713906750 q^{91} + 857134080 q^{92} - 50104019020 q^{93} - 46435766080 q^{94} - 59279283030 q^{95} - 42367168360 q^{97} + 83932761900 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(22))\)

We only show spaces with odd 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
22.11.b \(\chi_{22}(21, \cdot)\) 22.11.b.a 10 1
22.11.d \(\chi_{22}(7, \cdot)\) 22.11.d.a 40 4

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

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