Properties

Label 16.5.f
Level 16
Weight 5
Character orbit f
Rep. character \(\chi_{16}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 14
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 5 \)
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: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(16, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

\(14q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 64q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 92q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 64q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 92q^{8} \) \(\mathstrut -\mathstrut 100q^{10} \) \(\mathstrut +\mathstrut 94q^{11} \) \(\mathstrut -\mathstrut 332q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 44q^{14} \) \(\mathstrut -\mathstrut 168q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 1390q^{18} \) \(\mathstrut -\mathstrut 706q^{19} \) \(\mathstrut +\mathstrut 1900q^{20} \) \(\mathstrut -\mathstrut 164q^{21} \) \(\mathstrut +\mathstrut 900q^{22} \) \(\mathstrut +\mathstrut 1148q^{23} \) \(\mathstrut -\mathstrut 1872q^{24} \) \(\mathstrut -\mathstrut 3416q^{26} \) \(\mathstrut -\mathstrut 1664q^{27} \) \(\mathstrut -\mathstrut 3784q^{28} \) \(\mathstrut +\mathstrut 862q^{29} \) \(\mathstrut -\mathstrut 3740q^{30} \) \(\mathstrut +\mathstrut 3208q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 7508q^{34} \) \(\mathstrut +\mathstrut 1340q^{35} \) \(\mathstrut +\mathstrut 11468q^{36} \) \(\mathstrut -\mathstrut 1826q^{37} \) \(\mathstrut +\mathstrut 3568q^{38} \) \(\mathstrut +\mathstrut 2684q^{39} \) \(\mathstrut -\mathstrut 5144q^{40} \) \(\mathstrut -\mathstrut 17064q^{42} \) \(\mathstrut +\mathstrut 1694q^{43} \) \(\mathstrut -\mathstrut 14636q^{44} \) \(\mathstrut +\mathstrut 1410q^{45} \) \(\mathstrut -\mathstrut 5316q^{46} \) \(\mathstrut +\mathstrut 6888q^{48} \) \(\mathstrut +\mathstrut 682q^{49} \) \(\mathstrut +\mathstrut 20070q^{50} \) \(\mathstrut -\mathstrut 3012q^{51} \) \(\mathstrut +\mathstrut 20452q^{52} \) \(\mathstrut -\mathstrut 482q^{53} \) \(\mathstrut +\mathstrut 10784q^{54} \) \(\mathstrut -\mathstrut 11780q^{55} \) \(\mathstrut -\mathstrut 6952q^{56} \) \(\mathstrut -\mathstrut 20456q^{58} \) \(\mathstrut -\mathstrut 2786q^{59} \) \(\mathstrut -\mathstrut 29920q^{60} \) \(\mathstrut -\mathstrut 3778q^{61} \) \(\mathstrut -\mathstrut 11472q^{62} \) \(\mathstrut +\mathstrut 15808q^{64} \) \(\mathstrut -\mathstrut 2020q^{65} \) \(\mathstrut +\mathstrut 30148q^{66} \) \(\mathstrut +\mathstrut 7998q^{67} \) \(\mathstrut +\mathstrut 18032q^{68} \) \(\mathstrut +\mathstrut 9628q^{69} \) \(\mathstrut +\mathstrut 15296q^{70} \) \(\mathstrut +\mathstrut 19964q^{71} \) \(\mathstrut -\mathstrut 17708q^{72} \) \(\mathstrut -\mathstrut 23780q^{74} \) \(\mathstrut +\mathstrut 17570q^{75} \) \(\mathstrut -\mathstrut 23996q^{76} \) \(\mathstrut -\mathstrut 9508q^{77} \) \(\mathstrut -\mathstrut 8052q^{78} \) \(\mathstrut +\mathstrut 1384q^{80} \) \(\mathstrut +\mathstrut 1454q^{81} \) \(\mathstrut +\mathstrut 16016q^{82} \) \(\mathstrut -\mathstrut 17282q^{83} \) \(\mathstrut +\mathstrut 19624q^{84} \) \(\mathstrut +\mathstrut 9948q^{85} \) \(\mathstrut -\mathstrut 4796q^{86} \) \(\mathstrut -\mathstrut 49284q^{87} \) \(\mathstrut +\mathstrut 7288q^{88} \) \(\mathstrut -\mathstrut 5416q^{90} \) \(\mathstrut -\mathstrut 28036q^{91} \) \(\mathstrut -\mathstrut 14632q^{92} \) \(\mathstrut +\mathstrut 8896q^{93} \) \(\mathstrut +\mathstrut 432q^{94} \) \(\mathstrut +\mathstrut 6064q^{96} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 12246q^{98} \) \(\mathstrut +\mathstrut 49214q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(16, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
16.5.f.a \(14\) \(1.654\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(-4\) \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots\)