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Properties

Label 16.3
Level 16
Weight 3
Dimension 7
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(16))\).

Total New Old
Modular forms 23 11 12
Cusp forms 9 7 2
Eisenstein series 14 4 10

Trace form

\( 7 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 9 q^{9} + O(q^{10}) \) \( 7 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 9 q^{9} + 36 q^{10} - 18 q^{11} + 52 q^{12} + 8 q^{13} + 12 q^{14} - 40 q^{16} - 34 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21} - 52 q^{22} + 60 q^{23} + 48 q^{24} + 11 q^{25} + 96 q^{26} + 64 q^{27} + 56 q^{28} + 24 q^{29} + 52 q^{30} + 8 q^{32} - 4 q^{33} - 76 q^{34} - 100 q^{35} - 52 q^{36} - 24 q^{37} + 40 q^{38} - 196 q^{39} + 40 q^{40} + 18 q^{41} - 24 q^{42} - 114 q^{43} + 20 q^{44} + 12 q^{45} + 28 q^{46} - 24 q^{48} + 3 q^{49} + 46 q^{50} + 156 q^{51} + 100 q^{52} + 168 q^{53} + 32 q^{54} + 252 q^{55} - 168 q^{56} - 176 q^{58} + 206 q^{59} - 160 q^{60} + 8 q^{61} - 144 q^{62} + 64 q^{64} - 48 q^{65} + 196 q^{66} - 226 q^{67} + 112 q^{68} - 116 q^{69} - 16 q^{70} - 260 q^{71} + 52 q^{72} - 110 q^{73} - 92 q^{74} - 238 q^{75} - 188 q^{76} - 212 q^{77} - 84 q^{78} + 232 q^{80} + 167 q^{81} + 304 q^{82} + 318 q^{83} + 232 q^{84} - 32 q^{85} + 268 q^{86} + 444 q^{87} - 8 q^{88} - 78 q^{89} - 160 q^{90} + 188 q^{91} - 168 q^{92} - 32 q^{93} + 48 q^{94} - 80 q^{96} + 126 q^{97} + 10 q^{98} - 226 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)

We only show spaces with odd 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
16.3.c \(\chi_{16}(15, \cdot)\) 16.3.c.a 1 1
16.3.d \(\chi_{16}(7, \cdot)\) None 0 1
16.3.f \(\chi_{16}(3, \cdot)\) 16.3.f.a 6 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

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