Properties

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

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
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

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

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 the 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

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