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Properties

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

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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