Properties

Label 22.3
Level 22
Weight 3
Dimension 10
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 90
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(22))\).

Total New Old
Modular forms 40 10 30
Cusp forms 20 10 10
Eisenstein series 20 0 20

Trace form

\( 10 q - 20 q^{6} - 30 q^{7} - 20 q^{9} + O(q^{10}) \) \( 10 q - 20 q^{6} - 30 q^{7} - 20 q^{9} + 10 q^{11} + 20 q^{12} + 30 q^{13} + 40 q^{14} + 40 q^{15} + 30 q^{17} + 40 q^{18} - 30 q^{19} - 70 q^{23} - 40 q^{24} - 60 q^{25} - 120 q^{26} - 60 q^{27} - 40 q^{28} - 10 q^{29} - 60 q^{30} + 80 q^{31} + 40 q^{34} + 70 q^{35} + 20 q^{36} + 100 q^{37} + 180 q^{38} + 130 q^{39} + 80 q^{40} + 250 q^{41} + 80 q^{42} - 40 q^{44} - 120 q^{45} - 160 q^{46} - 170 q^{47} - 190 q^{49} - 80 q^{50} - 30 q^{51} - 40 q^{52} - 270 q^{53} - 40 q^{55} - 130 q^{57} + 160 q^{58} - 60 q^{59} + 120 q^{60} + 50 q^{61} + 20 q^{62} - 20 q^{63} - 160 q^{66} + 290 q^{67} + 60 q^{68} + 110 q^{69} - 20 q^{70} + 40 q^{71} - 80 q^{72} - 70 q^{73} - 40 q^{74} + 270 q^{75} + 410 q^{77} + 80 q^{78} + 370 q^{79} + 40 q^{80} + 290 q^{81} - 120 q^{82} - 150 q^{83} - 120 q^{84} - 330 q^{85} - 120 q^{86} + 120 q^{88} - 170 q^{89} + 160 q^{90} - 150 q^{91} - 180 q^{92} - 100 q^{93} - 20 q^{94} - 330 q^{95} - 260 q^{97} - 420 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
22.3.b \(\chi_{22}(21, \cdot)\) 22.3.b.a 2 1
22.3.d \(\chi_{22}(7, \cdot)\) 22.3.d.a 8 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)