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Properties

Label 16.22
Level 16
Weight 22
Dimension 92
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 352
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(16))\).

Total New Old
Modular forms 175 97 78
Cusp forms 161 92 69
Eisenstein series 14 5 9

Trace form

\( 92 q - 2 q^{2} - 59050 q^{3} + 1604328 q^{4} - 10391782 q^{5} - 142760912 q^{6} - 286396624 q^{7} - 5437750796 q^{8} + 36243817378 q^{9} + O(q^{10}) \) \( 92 q - 2 q^{2} - 59050 q^{3} + 1604328 q^{4} - 10391782 q^{5} - 142760912 q^{6} - 286396624 q^{7} - 5437750796 q^{8} + 36243817378 q^{9} - 101897120756 q^{10} + 23187707306 q^{11} + 366511438084 q^{12} - 53827631702 q^{13} + 3790342566044 q^{14} + 4204168998804 q^{15} + 1247007918232 q^{16} - 1849642826192 q^{17} + 24726998263422 q^{18} - 110453352648322 q^{19} - 3577794932068 q^{20} - 6314117754716 q^{21} - 275054389764220 q^{22} + 333505906879376 q^{23} - 568150485016400 q^{24} + 512198372079702 q^{25} + 2739706465705224 q^{26} - 2031951995590936 q^{27} - 5464734252855976 q^{28} + 1906781682488882 q^{29} + 1091847142900116 q^{30} - 10379756555051088 q^{31} + 21628424902862408 q^{32} + 277341305837020 q^{33} - 32599417569463756 q^{34} - 2910464255249188 q^{35} + 68896817700003052 q^{36} - 26709495884416190 q^{37} - 75508854642654272 q^{38} - 61106929702818224 q^{39} - 123452072199704568 q^{40} - 54372406343966748 q^{41} + 521576550189477880 q^{42} + 319855268707351986 q^{43} + 43551785926057540 q^{44} - 104214045481740882 q^{45} - 217010424311981172 q^{46} + 1926766754298531760 q^{47} - 791686606171970072 q^{48} - 5304291013702660240 q^{49} + 1308434315006519430 q^{50} + 1538865011057292404 q^{51} - 3929932006670549324 q^{52} + 1879807372131583378 q^{53} + 2474850774763823392 q^{54} - 1215488655761389904 q^{55} + 969847555025010328 q^{56} + 1041229908777309472 q^{57} - 13207633157582037672 q^{58} + 5292818428501253122 q^{59} + 19454740864921105152 q^{60} + 12274132836648867898 q^{61} - 231078435860679632 q^{62} - 29715678777691621644 q^{63} - 28922248017206732928 q^{64} - 1966809032340867860 q^{65} - 1066134537943733516 q^{66} + 9473816137519587854 q^{67} + 1578771419266928720 q^{68} - 32786555343493342380 q^{69} + 37884335466111605120 q^{70} + 41200641038922856624 q^{71} + 50190251198750321124 q^{72} - 37765020242610577116 q^{73} - 146575569503312954228 q^{74} + 71981443439667906318 q^{75} + 205207294437244346196 q^{76} - 57650157685559592028 q^{77} + 18923646523591896860 q^{78} + 218347767667773487456 q^{79} - 129507348099746628056 q^{80} - 568232602850197295244 q^{81} + 830734363602759714528 q^{82} + 270436356780641410870 q^{83} - 1733590905678879817304 q^{84} + 79572141783003211996 q^{85} + 1244418239240036417540 q^{86} - 227604522934813134384 q^{87} + 1366637891097356775928 q^{88} - 240584055283923843516 q^{89} - 4303359727133135334888 q^{90} + 547037216788540754084 q^{91} + 3708288645268614974264 q^{92} + 243743820035119439312 q^{93} - 1146977544252955048048 q^{94} - 1387742098117320389948 q^{95} - 1490348200640250797392 q^{96} + 710462713306615232464 q^{97} + 7549812802452897368090 q^{98} + 1934499911809701436966 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(16))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
16.22.a \(\chi_{16}(1, \cdot)\) 16.22.a.a 1 1
16.22.a.b 1
16.22.a.c 1
16.22.a.d 2
16.22.a.e 2
16.22.a.f 3
16.22.b \(\chi_{16}(9, \cdot)\) None 0 1
16.22.e \(\chi_{16}(5, \cdot)\) 16.22.e.a 82 2

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 1}\)