Properties

Label 16.4.e
Level 16
Weight 4
Character orbit e
Rep. character \(\chi_{16}(5,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 10
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 16 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(16, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\(10q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 32q^{6} \) \(\mathstrut -\mathstrut 44q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 32q^{6} \) \(\mathstrut -\mathstrut 44q^{8} \) \(\mathstrut -\mathstrut 68q^{10} \) \(\mathstrut +\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 100q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 188q^{14} \) \(\mathstrut -\mathstrut 124q^{15} \) \(\mathstrut +\mathstrut 280q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 174q^{18} \) \(\mathstrut -\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 196q^{20} \) \(\mathstrut +\mathstrut 52q^{21} \) \(\mathstrut -\mathstrut 588q^{22} \) \(\mathstrut -\mathstrut 848q^{24} \) \(\mathstrut -\mathstrut 264q^{26} \) \(\mathstrut +\mathstrut 184q^{27} \) \(\mathstrut +\mathstrut 280q^{28} \) \(\mathstrut -\mathstrut 202q^{29} \) \(\mathstrut +\mathstrut 1236q^{30} \) \(\mathstrut +\mathstrut 368q^{31} \) \(\mathstrut +\mathstrut 968q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 436q^{34} \) \(\mathstrut +\mathstrut 476q^{35} \) \(\mathstrut -\mathstrut 596q^{36} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 1232q^{38} \) \(\mathstrut -\mathstrut 1336q^{40} \) \(\mathstrut -\mathstrut 680q^{42} \) \(\mathstrut -\mathstrut 838q^{43} \) \(\mathstrut +\mathstrut 868q^{44} \) \(\mathstrut +\mathstrut 194q^{45} \) \(\mathstrut +\mathstrut 1132q^{46} \) \(\mathstrut -\mathstrut 944q^{47} \) \(\mathstrut +\mathstrut 1768q^{48} \) \(\mathstrut +\mathstrut 94q^{49} \) \(\mathstrut +\mathstrut 726q^{50} \) \(\mathstrut -\mathstrut 1500q^{51} \) \(\mathstrut -\mathstrut 236q^{52} \) \(\mathstrut -\mathstrut 378q^{53} \) \(\mathstrut -\mathstrut 1376q^{54} \) \(\mathstrut -\mathstrut 488q^{56} \) \(\mathstrut +\mathstrut 8q^{58} \) \(\mathstrut +\mathstrut 1706q^{59} \) \(\mathstrut -\mathstrut 192q^{60} \) \(\mathstrut +\mathstrut 910q^{61} \) \(\mathstrut -\mathstrut 80q^{62} \) \(\mathstrut +\mathstrut 2628q^{63} \) \(\mathstrut +\mathstrut 512q^{64} \) \(\mathstrut -\mathstrut 492q^{65} \) \(\mathstrut -\mathstrut 428q^{66} \) \(\mathstrut +\mathstrut 1942q^{67} \) \(\mathstrut -\mathstrut 880q^{68} \) \(\mathstrut +\mathstrut 580q^{69} \) \(\mathstrut +\mathstrut 160q^{70} \) \(\mathstrut +\mathstrut 1092q^{72} \) \(\mathstrut -\mathstrut 452q^{74} \) \(\mathstrut -\mathstrut 2954q^{75} \) \(\mathstrut -\mathstrut 1228q^{76} \) \(\mathstrut -\mathstrut 268q^{77} \) \(\mathstrut -\mathstrut 772q^{78} \) \(\mathstrut -\mathstrut 4416q^{79} \) \(\mathstrut -\mathstrut 2648q^{80} \) \(\mathstrut +\mathstrut 482q^{81} \) \(\mathstrut -\mathstrut 704q^{82} \) \(\mathstrut -\mathstrut 2562q^{83} \) \(\mathstrut +\mathstrut 1960q^{84} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 3764q^{86} \) \(\mathstrut +\mathstrut 1528q^{88} \) \(\mathstrut +\mathstrut 1896q^{90} \) \(\mathstrut +\mathstrut 3332q^{91} \) \(\mathstrut +\mathstrut 632q^{92} \) \(\mathstrut -\mathstrut 2192q^{93} \) \(\mathstrut -\mathstrut 3248q^{94} \) \(\mathstrut +\mathstrut 6900q^{95} \) \(\mathstrut -\mathstrut 4432q^{96} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut 314q^{98} \) \(\mathstrut +\mathstrut 4958q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(16, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
16.4.e.a \(10\) \(0.944\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)