Properties

Label 16.12
Level 16
Weight 12
Dimension 47
Nonzero newspaces 2
Newforms 5
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(16))\).

Total New Old
Modular forms 95 52 43
Cusp forms 81 47 34
Eisenstein series 14 5 9

Trace form

\( 47q - 2q^{2} + 242q^{3} + 3080q^{4} - 1324q^{5} + 30352q^{6} - 68152q^{7} + 74836q^{8} + 339817q^{9} + O(q^{10}) \) \( 47q - 2q^{2} + 242q^{3} + 3080q^{4} - 1324q^{5} + 30352q^{6} - 68152q^{7} + 74836q^{8} + 339817q^{9} - 988948q^{10} - 328114q^{11} + 2300260q^{12} + 123020q^{13} - 1829956q^{14} - 2356452q^{15} - 3721448q^{16} + 2386294q^{17} - 32219106q^{18} + 2660842q^{19} + 68655164q^{20} + 12743188q^{21} - 85011388q^{22} - 15109672q^{23} - 66180944q^{24} + 61783619q^{25} + 305685384q^{26} - 106529152q^{27} - 322075880q^{28} - 105393292q^{29} + 290643636q^{30} + 240250768q^{31} + 404698568q^{32} - 298469780q^{33} - 882461836q^{34} + 63565004q^{35} + 1854387628q^{36} - 175835796q^{37} - 1276252832q^{38} - 1570233992q^{39} - 483241016q^{40} + 62633826q^{41} + 2372079160q^{42} + 5618204310q^{43} - 2657283740q^{44} + 748915536q^{45} - 1032658964q^{46} - 6695893376q^{47} - 1058870552q^{48} - 6852667381q^{49} + 6515930886q^{50} + 17628376652q^{51} - 13915491564q^{52} - 3121712276q^{53} + 4385621536q^{54} - 15975322488q^{55} + 12910845976q^{56} - 4106770544q^{57} - 21491153128q^{58} + 24222643990q^{59} + 25615752768q^{60} + 3412924524q^{61} - 15814519760q^{62} - 14986113876q^{63} + 9674332160q^{64} + 2653794424q^{65} + 10932459412q^{66} + 30094977866q^{67} + 13817664656q^{68} - 27669589788q^{69} - 27206453120q^{70} - 60900642296q^{71} - 20773133628q^{72} + 3416691010q^{73} + 14141420908q^{74} + 148589845602q^{75} - 11786004940q^{76} - 32553795820q^{77} + 37031200508q^{78} - 51552596208q^{79} - 8952586328q^{80} - 107271212433q^{81} - 81555388352q^{82} + 167445804226q^{83} + 61178517160q^{84} - 7709848192q^{85} + 10047297860q^{86} - 115244963016q^{87} - 162855622152q^{88} + 27045197490q^{89} + 160133627736q^{90} - 79241352396q^{91} - 169766721928q^{92} - 42015932560q^{93} + 160320530128q^{94} + 383528784748q^{95} + 230764310192q^{96} - 19977511002q^{97} - 108887063494q^{98} - 311242980470q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
16.12.a \(\chi_{16}(1, \cdot)\) 16.12.a.a 1 1
16.12.a.b 1
16.12.a.c 1
16.12.a.d 2
16.12.b \(\chi_{16}(9, \cdot)\) None 0 1
16.12.e \(\chi_{16}(5, \cdot)\) 16.12.e.a 42 2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)