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Properties

Label 16.3.f
Level $16$
Weight $3$
Character orbit 16.f
Rep. character $\chi_{16}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(16, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.3.f.a 16.f 16.f $6$ $0.436$ 6.0.399424.1 None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)