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Properties

Label 71.3.f
Level $71$
Weight $3$
Character orbit 71.f
Rep. character $\chi_{71}(23,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $66$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 71.f (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 71 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(71, [\chi])\).

Total New Old
Modular forms 78 78 0
Cusp forms 66 66 0
Eisenstein series 12 12 0

Trace form

\( 66 q - 3 q^{2} - 10 q^{3} - 31 q^{4} - 6 q^{5} - 3 q^{6} - 7 q^{7} - 11 q^{8} - 11 q^{9} + 28 q^{10} - 7 q^{11} + 8 q^{12} - 7 q^{13} - 128 q^{15} + 117 q^{16} - 229 q^{18} - 19 q^{19} + 74 q^{20} + 98 q^{21}+ \cdots + 889 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(71, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
71.3.f.a 71.f 71.f $66$ $1.935$ None 71.3.f.a \(-3\) \(-10\) \(-6\) \(-7\) $\mathrm{SU}(2)[C_{14}]$