Properties

Label 387.3.s
Level $387$
Weight $3$
Character orbit 387.s
Rep. character $\chi_{387}(85,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $172$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 387.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(387, [\chi])\).

Total New Old
Modular forms 180 180 0
Cusp forms 172 172 0
Eisenstein series 8 8 0

Trace form

\( 172 q + 166 q^{4} - 36 q^{6} + O(q^{10}) \) \( 172 q + 166 q^{4} - 36 q^{6} - 24 q^{10} + 10 q^{11} - 12 q^{13} + 6 q^{14} - 22 q^{15} - 314 q^{16} + 64 q^{17} - 14 q^{21} - 2 q^{23} - 14 q^{24} + 388 q^{25} + 30 q^{31} - 192 q^{35} + 368 q^{36} - 294 q^{38} - 158 q^{41} - 63 q^{43} + 184 q^{44} + 28 q^{47} + 538 q^{49} + 150 q^{52} + 352 q^{53} - 94 q^{54} - 18 q^{56} - 18 q^{58} + 28 q^{59} - 380 q^{60} - 1112 q^{64} + 162 q^{66} + 12 q^{67} - 428 q^{68} - 468 q^{74} + 868 q^{78} - 36 q^{79} + 56 q^{81} + 94 q^{83} - 772 q^{84} + 93 q^{86} - 138 q^{87} - 848 q^{90} + 574 q^{92} - 60 q^{95} + 1066 q^{96} - 220 q^{97} + 406 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
387.3.s.a 387.s 387.s $172$ $10.545$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$