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

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

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

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