Properties

Label 22.4
Level 22
Weight 4
Dimension 15
Nonzero newspaces 2
Newforms 5
Sturm bound 120
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(22))\).

Total New Old
Modular forms 55 15 40
Cusp forms 35 15 20
Eisenstein series 20 0 20

Trace form

\(15q \) \(\mathstrut +\mathstrut 50q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut -\mathstrut 160q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 50q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut -\mathstrut 160q^{9} \) \(\mathstrut -\mathstrut 100q^{10} \) \(\mathstrut -\mathstrut 100q^{11} \) \(\mathstrut -\mathstrut 80q^{12} \) \(\mathstrut -\mathstrut 40q^{13} \) \(\mathstrut +\mathstrut 20q^{14} \) \(\mathstrut +\mathstrut 410q^{15} \) \(\mathstrut +\mathstrut 310q^{17} \) \(\mathstrut +\mathstrut 230q^{18} \) \(\mathstrut -\mathstrut 225q^{19} \) \(\mathstrut -\mathstrut 420q^{21} \) \(\mathstrut +\mathstrut 390q^{23} \) \(\mathstrut +\mathstrut 200q^{24} \) \(\mathstrut +\mathstrut 300q^{25} \) \(\mathstrut +\mathstrut 200q^{26} \) \(\mathstrut +\mathstrut 75q^{27} \) \(\mathstrut -\mathstrut 120q^{28} \) \(\mathstrut -\mathstrut 250q^{29} \) \(\mathstrut -\mathstrut 780q^{30} \) \(\mathstrut +\mathstrut 90q^{31} \) \(\mathstrut -\mathstrut 160q^{32} \) \(\mathstrut -\mathstrut 1265q^{33} \) \(\mathstrut -\mathstrut 600q^{34} \) \(\mathstrut -\mathstrut 1010q^{35} \) \(\mathstrut -\mathstrut 100q^{36} \) \(\mathstrut -\mathstrut 240q^{37} \) \(\mathstrut -\mathstrut 60q^{38} \) \(\mathstrut -\mathstrut 160q^{39} \) \(\mathstrut +\mathstrut 240q^{40} \) \(\mathstrut +\mathstrut 830q^{41} \) \(\mathstrut +\mathstrut 2180q^{42} \) \(\mathstrut +\mathstrut 2690q^{43} \) \(\mathstrut +\mathstrut 1060q^{44} \) \(\mathstrut +\mathstrut 1910q^{45} \) \(\mathstrut +\mathstrut 360q^{46} \) \(\mathstrut -\mathstrut 250q^{47} \) \(\mathstrut -\mathstrut 1330q^{49} \) \(\mathstrut -\mathstrut 680q^{50} \) \(\mathstrut -\mathstrut 695q^{51} \) \(\mathstrut -\mathstrut 960q^{52} \) \(\mathstrut +\mathstrut 260q^{53} \) \(\mathstrut -\mathstrut 2160q^{54} \) \(\mathstrut -\mathstrut 370q^{55} \) \(\mathstrut -\mathstrut 945q^{57} \) \(\mathstrut -\mathstrut 1680q^{58} \) \(\mathstrut -\mathstrut 1825q^{59} \) \(\mathstrut -\mathstrut 480q^{60} \) \(\mathstrut +\mathstrut 260q^{61} \) \(\mathstrut +\mathstrut 1380q^{62} \) \(\mathstrut +\mathstrut 1720q^{63} \) \(\mathstrut +\mathstrut 760q^{65} \) \(\mathstrut +\mathstrut 2920q^{66} \) \(\mathstrut +\mathstrut 820q^{67} \) \(\mathstrut +\mathstrut 1240q^{68} \) \(\mathstrut +\mathstrut 840q^{70} \) \(\mathstrut -\mathstrut 3240q^{71} \) \(\mathstrut -\mathstrut 1120q^{72} \) \(\mathstrut -\mathstrut 870q^{73} \) \(\mathstrut -\mathstrut 1400q^{74} \) \(\mathstrut -\mathstrut 5045q^{75} \) \(\mathstrut -\mathstrut 760q^{76} \) \(\mathstrut +\mathstrut 630q^{77} \) \(\mathstrut -\mathstrut 2960q^{78} \) \(\mathstrut +\mathstrut 240q^{79} \) \(\mathstrut -\mathstrut 640q^{80} \) \(\mathstrut +\mathstrut 2505q^{81} \) \(\mathstrut +\mathstrut 1690q^{82} \) \(\mathstrut +\mathstrut 4445q^{83} \) \(\mathstrut +\mathstrut 1840q^{84} \) \(\mathstrut +\mathstrut 2420q^{85} \) \(\mathstrut +\mathstrut 2450q^{86} \) \(\mathstrut +\mathstrut 3400q^{87} \) \(\mathstrut +\mathstrut 560q^{88} \) \(\mathstrut +\mathstrut 350q^{89} \) \(\mathstrut +\mathstrut 2940q^{90} \) \(\mathstrut +\mathstrut 3830q^{91} \) \(\mathstrut -\mathstrut 1680q^{92} \) \(\mathstrut +\mathstrut 6230q^{93} \) \(\mathstrut -\mathstrut 1600q^{94} \) \(\mathstrut -\mathstrut 2200q^{95} \) \(\mathstrut -\mathstrut 3345q^{97} \) \(\mathstrut -\mathstrut 4410q^{98} \) \(\mathstrut -\mathstrut 7790q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
22.4.a \(\chi_{22}(1, \cdot)\) 22.4.a.a 1 1
22.4.a.b 1
22.4.a.c 1
22.4.c \(\chi_{22}(3, \cdot)\) 22.4.c.a 4 4
22.4.c.b 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

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