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Properties

Label 22.15
Level 22
Weight 15
Dimension 70
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 450
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(450\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(22))\).

Total New Old
Modular forms 220 70 150
Cusp forms 200 70 130
Eisenstein series 20 0 20

Trace form

\( 70 q - 715520 q^{6} - 3150030 q^{7} - 23137940 q^{9} + O(q^{10}) \) \( 70 q - 715520 q^{6} - 3150030 q^{7} - 23137940 q^{9} + 50736410 q^{11} - 88391680 q^{12} - 52191330 q^{13} + 333063680 q^{14} - 336419360 q^{15} + 1057763310 q^{17} - 2162301440 q^{18} + 312644670 q^{19} + 21436225090 q^{23} - 5861539840 q^{24} + 20571103140 q^{25} - 22591787520 q^{26} - 19915434240 q^{27} + 20815708160 q^{28} + 36692789590 q^{29} - 65862447360 q^{30} - 83868673720 q^{31} + 289566594900 q^{33} + 121766295040 q^{34} - 121345288330 q^{35} - 69193646080 q^{36} - 118533868700 q^{37} + 471450458880 q^{38} + 1166701695250 q^{39} - 53708062720 q^{40} - 1527743287870 q^{41} + 457168378880 q^{42} + 356224860160 q^{44} + 1425062258880 q^{45} - 890637752320 q^{46} - 3070788294250 q^{47} + 4687753533770 q^{49} + 1765293470720 q^{50} + 700577648910 q^{51} - 2677054013440 q^{52} - 8762994290190 q^{53} + 13191150693560 q^{55} - 11387609854270 q^{57} - 6572629207040 q^{58} - 2645396883720 q^{59} - 5142222766080 q^{60} + 18360802231730 q^{61} + 6005140806400 q^{62} - 14288180427380 q^{63} - 20875055134720 q^{66} + 22636571179250 q^{67} + 8665197035520 q^{68} - 2660180650930 q^{69} + 243848961280 q^{70} - 3058953591160 q^{71} + 4584563015680 q^{72} - 26828424156910 q^{73} - 28392198448640 q^{74} - 41585517646830 q^{75} - 68641639610750 q^{77} + 80058611870720 q^{78} + 54712617735250 q^{79} - 375138549760 q^{80} + 84384096494150 q^{81} - 103920375636480 q^{82} - 118385967772650 q^{83} + 41564059238400 q^{84} + 295368811385670 q^{85} + 203900873909760 q^{86} - 16257405419520 q^{88} - 241697517422770 q^{89} - 190230773565440 q^{90} + 487742682936450 q^{91} + 177574884065280 q^{92} - 40890903687220 q^{93} - 224981452901120 q^{94} - 285342982769130 q^{95} - 214409980584560 q^{97} + 5765782662660 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.15.b \(\chi_{22}(21, \cdot)\) 22.15.b.a 14 1
22.15.d \(\chi_{22}(7, \cdot)\) 22.15.d.a 56 4

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)