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Properties

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

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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