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Properties

Label 16.18
Level 16
Weight 18
Dimension 74
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(16))\).

Total New Old
Modular forms 143 79 64
Cusp forms 129 74 55
Eisenstein series 14 5 9

Trace form

\( 74 q - 2 q^{2} - 6562 q^{3} - 54744 q^{4} - 12242 q^{5} - 9659408 q^{6} + 13155520 q^{7} - 101532236 q^{8} + 381202024 q^{9} + O(q^{10}) \) \( 74 q - 2 q^{2} - 6562 q^{3} - 54744 q^{4} - 12242 q^{5} - 9659408 q^{6} + 13155520 q^{7} - 101532236 q^{8} + 381202024 q^{9} + 284165324 q^{10} - 629746270 q^{11} + 647301316 q^{12} - 795138962 q^{13} + 6580735964 q^{14} + 43357282884 q^{15} + 49260326296 q^{16} + 9464779916 q^{17} - 154774440258 q^{18} - 160260341018 q^{19} + 534629724892 q^{20} - 127977749372 q^{21} + 344069189380 q^{22} - 169801828800 q^{23} - 1845764583248 q^{24} + 327793560312 q^{25} + 3054933980680 q^{26} - 895065396808 q^{27} - 3163268182312 q^{28} - 3747885438858 q^{29} + 1112739979476 q^{30} - 12582925000976 q^{31} - 14092609233592 q^{32} - 195602811524 q^{33} + 4421458841268 q^{34} - 42636908870788 q^{35} - 78648071112596 q^{36} - 29610623095114 q^{37} + 26879344539648 q^{38} + 40546924882240 q^{39} + 78479998694792 q^{40} - 9753146876592 q^{41} - 280546585448840 q^{42} + 61410640185770 q^{43} + 353399653694852 q^{44} - 18045065496462 q^{45} - 205880797854900 q^{46} + 259006469750416 q^{47} - 336693732420632 q^{48} - 1370075944811378 q^{49} + 633347781304710 q^{50} + 507539017453508 q^{51} - 250572184348044 q^{52} - 1382682749134810 q^{53} + 1545312889650976 q^{54} + 453009721885376 q^{55} + 1727282544382360 q^{56} - 1096531773403520 q^{57} - 4743213379910952 q^{58} - 3791819174161638 q^{59} + 12475663393894272 q^{60} + 4331243185960670 q^{61} - 1023265995226064 q^{62} - 2157599059654716 q^{63} - 4803736754115456 q^{64} + 2429294956866340 q^{65} + 34592600807745844 q^{66} + 8347599866621270 q^{67} - 30604279033681200 q^{68} - 16045751573030028 q^{69} + 24438949220497280 q^{70} - 6110717387570496 q^{71} + 30860656197322404 q^{72} - 9399120337579440 q^{73} - 48718480417927860 q^{74} - 46430308023123162 q^{75} + 43334084125892628 q^{76} + 30874630657902724 q^{77} - 3562265224457764 q^{78} - 389424450361984 q^{79} + 5755873605839144 q^{80} - 82391387373730158 q^{81} + 16449314794081440 q^{82} - 129539042555089442 q^{83} + 1829809934827432 q^{84} - 47862322723929884 q^{85} - 17054234444405628 q^{86} + 57285930233352000 q^{87} + 67522006496247288 q^{88} - 17574490465707312 q^{89} + 157628356281694872 q^{90} + 92783259041889924 q^{91} - 64767112552277064 q^{92} - 35713337594727664 q^{93} + 12145263016662032 q^{94} - 355469009965492428 q^{95} + 92392677588189872 q^{96} - 71510264285450484 q^{97} + 38163698339299674 q^{98} + 164675678974086046 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.18.a \(\chi_{16}(1, \cdot)\) 16.18.a.a 1 1
16.18.a.b 1
16.18.a.c 2
16.18.a.d 2
16.18.a.e 2
16.18.b \(\chi_{16}(9, \cdot)\) None 0 1
16.18.e \(\chi_{16}(5, \cdot)\) 16.18.e.a 66 2

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 1}\)