Properties

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

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
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

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

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

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