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

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

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

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