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Properties

Label 731.2.s
Level $731$
Weight $2$
Character orbit 731.s
Rep. character $\chi_{731}(214,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $512$
Newform subspaces $2$
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: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
731.2.s.a 731.s 731.s $16$ $5.837$ 16.0.\(\cdots\).1 \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{16}]$ \(q+2\beta _{4}q^{4}-3\beta _{5}q^{9}+(-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{11}+\cdots\)
731.2.s.b 731.s 731.s $496$ $5.837$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$