Properties

Label 16.3.f
Level 16
Weight 3
Character orbit f
Rep. character \(\chi_{16}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 6
Newforms 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: \(\Q(i)\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(16, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
16.3.f.a \(6\) \(0.436\) 6.0.399424.1 None \(-2\) \(-2\) \(-2\) \(-4\) \(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)