Properties

Label 22.7
Level 22
Weight 7
Dimension 30
Nonzero newspaces 2
Newforms 2
Sturm bound 210
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(210\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(22))\).

Total New Old
Modular forms 100 30 70
Cusp forms 80 30 50
Eisenstein series 20 0 20

Trace form

\(30q \) \(\mathstrut +\mathstrut 400q^{6} \) \(\mathstrut +\mathstrut 720q^{7} \) \(\mathstrut -\mathstrut 4160q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 400q^{6} \) \(\mathstrut +\mathstrut 720q^{7} \) \(\mathstrut -\mathstrut 4160q^{9} \) \(\mathstrut +\mathstrut 3200q^{11} \) \(\mathstrut +\mathstrut 5120q^{12} \) \(\mathstrut +\mathstrut 3600q^{13} \) \(\mathstrut -\mathstrut 2080q^{14} \) \(\mathstrut -\mathstrut 8660q^{15} \) \(\mathstrut -\mathstrut 5880q^{17} \) \(\mathstrut +\mathstrut 18400q^{18} \) \(\mathstrut -\mathstrut 23850q^{19} \) \(\mathstrut -\mathstrut 37940q^{23} \) \(\mathstrut +\mathstrut 12800q^{24} \) \(\mathstrut +\mathstrut 129840q^{25} \) \(\mathstrut +\mathstrut 50400q^{26} \) \(\mathstrut -\mathstrut 53250q^{27} \) \(\mathstrut -\mathstrut 32640q^{28} \) \(\mathstrut -\mathstrut 204800q^{29} \) \(\mathstrut -\mathstrut 134160q^{30} \) \(\mathstrut -\mathstrut 6900q^{31} \) \(\mathstrut +\mathstrut 153450q^{33} \) \(\mathstrut +\mathstrut 117600q^{34} \) \(\mathstrut +\mathstrut 469520q^{35} \) \(\mathstrut +\mathstrut 36800q^{36} \) \(\mathstrut +\mathstrut 103200q^{37} \) \(\mathstrut +\mathstrut 28080q^{38} \) \(\mathstrut -\mathstrut 328640q^{39} \) \(\mathstrut -\mathstrut 107520q^{40} \) \(\mathstrut -\mathstrut 541660q^{41} \) \(\mathstrut -\mathstrut 521920q^{42} \) \(\mathstrut +\mathstrut 251200q^{44} \) \(\mathstrut +\mathstrut 1180380q^{45} \) \(\mathstrut +\mathstrut 213120q^{46} \) \(\mathstrut +\mathstrut 193640q^{47} \) \(\mathstrut -\mathstrut 645420q^{49} \) \(\mathstrut -\mathstrut 364480q^{50} \) \(\mathstrut -\mathstrut 1347330q^{51} \) \(\mathstrut -\mathstrut 291840q^{52} \) \(\mathstrut +\mathstrut 81120q^{53} \) \(\mathstrut +\mathstrut 714960q^{55} \) \(\mathstrut +\mathstrut 1416050q^{57} \) \(\mathstrut +\mathstrut 1061760q^{58} \) \(\mathstrut +\mathstrut 94170q^{59} \) \(\mathstrut +\mathstrut 414720q^{60} \) \(\mathstrut -\mathstrut 1184160q^{61} \) \(\mathstrut -\mathstrut 226640q^{62} \) \(\mathstrut -\mathstrut 921200q^{63} \) \(\mathstrut +\mathstrut 321920q^{66} \) \(\mathstrut +\mathstrut 22320q^{67} \) \(\mathstrut -\mathstrut 188160q^{68} \) \(\mathstrut +\mathstrut 1356080q^{69} \) \(\mathstrut +\mathstrut 304080q^{70} \) \(\mathstrut -\mathstrut 242800q^{71} \) \(\mathstrut -\mathstrut 896000q^{72} \) \(\mathstrut -\mathstrut 590340q^{73} \) \(\mathstrut -\mathstrut 610400q^{74} \) \(\mathstrut -\mathstrut 2419830q^{75} \) \(\mathstrut -\mathstrut 1972220q^{77} \) \(\mathstrut +\mathstrut 1361600q^{78} \) \(\mathstrut +\mathstrut 93240q^{79} \) \(\mathstrut +\mathstrut 573440q^{80} \) \(\mathstrut +\mathstrut 1519730q^{81} \) \(\mathstrut +\mathstrut 741600q^{82} \) \(\mathstrut +\mathstrut 4588350q^{83} \) \(\mathstrut +\mathstrut 2357760q^{84} \) \(\mathstrut +\mathstrut 4132920q^{85} \) \(\mathstrut +\mathstrut 2113440q^{86} \) \(\mathstrut -\mathstrut 806400q^{88} \) \(\mathstrut -\mathstrut 2260900q^{89} \) \(\mathstrut -\mathstrut 6535040q^{90} \) \(\mathstrut -\mathstrut 8984700q^{91} \) \(\mathstrut -\mathstrut 2419200q^{92} \) \(\mathstrut +\mathstrut 143240q^{93} \) \(\mathstrut -\mathstrut 2410800q^{94} \) \(\mathstrut +\mathstrut 661320q^{95} \) \(\mathstrut +\mathstrut 1009290q^{97} \) \(\mathstrut +\mathstrut 2419140q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.7.b \(\chi_{22}(21, \cdot)\) 22.7.b.a 6 1
22.7.d \(\chi_{22}(7, \cdot)\) 22.7.d.a 24 4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)