Properties

Label 731.2.s
Level 731
Weight 2
Character orbit s
Rep. character \(\chi_{731}(214,\cdot)\)
Character field \(\Q(\zeta_{16})\)
Dimension 512
Newforms 2
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.s (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 731 \)
Character field: \(\Q(\zeta_{16})\)
Newforms: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

Total New Old
Modular forms 544 544 0
Cusp forms 512 512 0
Eisenstein series 32 32 0

Trace form

\( 512q - 16q^{4} - 16q^{6} - 16q^{9} + O(q^{10}) \) \( 512q - 16q^{4} - 16q^{6} - 16q^{9} - 16q^{10} - 8q^{13} - 16q^{14} - 16q^{15} - 16q^{17} - 16q^{21} - 24q^{23} - 64q^{24} + 48q^{31} - 96q^{35} + 16q^{36} - 32q^{38} - 16q^{40} - 16q^{41} - 48q^{43} - 80q^{44} - 96q^{47} - 16q^{49} + 96q^{52} - 16q^{53} + 144q^{54} - 16q^{56} - 48q^{57} - 64q^{58} - 48q^{59} - 224q^{60} - 48q^{64} - 272q^{66} - 16q^{68} - 112q^{74} + 64q^{78} + 16q^{79} + 96q^{81} + 16q^{83} + 96q^{86} - 16q^{87} + 64q^{90} + 368q^{92} - 96q^{95} + 80q^{96} - 80q^{97} - 128q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
731.2.s.a \(16\) \(5.837\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{4}q^{4}-3\beta _{5}q^{9}+(-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{11}+\cdots\)
731.2.s.b \(496\) \(5.837\) None \(0\) \(0\) \(0\) \(0\)