↑

Properties

Label 16.6
Level 16
Weight 6
Dimension 20
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 96
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(16))\).

Total New Old
Modular forms 47 25 22
Cusp forms 33 20 13
Eisenstein series 14 5 9

Trace form

\( 20 q - 2 q^{2} - 10 q^{3} - 24 q^{4} - 22 q^{5} + 112 q^{6} + 112 q^{7} + 244 q^{8} + 58 q^{9} + O(q^{10}) \) \( 20 q - 2 q^{2} - 10 q^{3} - 24 q^{4} - 22 q^{5} + 112 q^{6} + 112 q^{7} + 244 q^{8} + 58 q^{9} - 436 q^{10} - 1270 q^{11} + 4 q^{12} + 58 q^{13} - 100 q^{14} + 3924 q^{15} - 872 q^{16} - 608 q^{17} - 3138 q^{18} - 6242 q^{19} + 2972 q^{20} + 1060 q^{21} + 4420 q^{22} + 3920 q^{23} + 8368 q^{24} + 2142 q^{25} + 7368 q^{26} + 1832 q^{27} - 7336 q^{28} + 194 q^{29} - 30444 q^{30} - 10064 q^{31} - 23992 q^{32} - 4004 q^{33} - 1740 q^{34} + 11612 q^{35} + 6892 q^{36} - 622 q^{37} + 53248 q^{38} - 14576 q^{39} + 75272 q^{40} + 8340 q^{41} + 33400 q^{42} + 5906 q^{43} - 40124 q^{44} - 11202 q^{45} - 92532 q^{46} + 21808 q^{47} - 147992 q^{48} - 39704 q^{49} - 85050 q^{50} + 28340 q^{51} + 91572 q^{52} + 55906 q^{53} + 208672 q^{54} - 19984 q^{55} + 191128 q^{56} + 50848 q^{57} + 106776 q^{58} - 38942 q^{59} - 154368 q^{60} - 101302 q^{61} - 273872 q^{62} - 17100 q^{63} - 283776 q^{64} - 30260 q^{65} - 153356 q^{66} - 81490 q^{67} + 133712 q^{68} + 75732 q^{69} + 412160 q^{70} + 78832 q^{71} + 470244 q^{72} + 62676 q^{73} + 147148 q^{74} + 105198 q^{75} - 87468 q^{76} - 9436 q^{77} - 631780 q^{78} - 20512 q^{79} - 554456 q^{80} - 110868 q^{81} - 93216 q^{82} + 92758 q^{83} + 190888 q^{84} - 17924 q^{85} + 470468 q^{86} + 58512 q^{87} + 590328 q^{88} + 101748 q^{89} + 280152 q^{90} - 256476 q^{91} - 221896 q^{92} + 15056 q^{93} - 460912 q^{94} - 70268 q^{95} - 597328 q^{96} - 73536 q^{97} - 444646 q^{98} - 262778 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.6.a \(\chi_{16}(1, \cdot)\) 16.6.a.a 1 1
16.6.a.b 1
16.6.b \(\chi_{16}(9, \cdot)\) None 0 1
16.6.e \(\chi_{16}(5, \cdot)\) 16.6.e.a 18 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)