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Properties

Label 22.5
Level 22
Weight 5
Dimension 20
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 150
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(150\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(22))\).

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

Trace form

\( 20 q - 80 q^{6} + 150 q^{7} + 340 q^{9} + O(q^{10}) \) \( 20 q - 80 q^{6} + 150 q^{7} + 340 q^{9} - 210 q^{11} - 400 q^{12} - 510 q^{13} - 480 q^{14} - 860 q^{15} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 3990 q^{23} - 640 q^{24} - 2580 q^{25} + 1920 q^{26} + 2730 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 5020 q^{31} - 4950 q^{33} - 2560 q^{34} - 8670 q^{35} - 1120 q^{36} - 4900 q^{37} - 7200 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 4000 q^{42} + 2160 q^{44} + 10980 q^{45} + 4480 q^{46} + 6330 q^{47} + 14530 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} - 5970 q^{53} + 1720 q^{55} + 9140 q^{57} - 16000 q^{58} + 3270 q^{59} - 10080 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 15680 q^{66} + 12790 q^{67} + 14160 q^{68} + 37730 q^{69} + 37280 q^{70} - 2040 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} - 5580 q^{75} - 3990 q^{77} - 12160 q^{78} - 2770 q^{79} - 5760 q^{80} - 56560 q^{81} - 37440 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} - 9840 q^{86} - 3840 q^{88} + 37830 q^{89} + 55360 q^{90} + 49650 q^{91} + 26640 q^{92} + 41180 q^{93} + 58880 q^{94} + 74250 q^{95} + 13550 q^{97} + 33240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.5.b \(\chi_{22}(21, \cdot)\) 22.5.b.a 4 1
22.5.d \(\chi_{22}(7, \cdot)\) 22.5.d.a 16 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)