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Properties

Label 171.4.e
Level $171$
Weight $4$
Character orbit 171.e
Rep. character $\chi_{171}(58,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $108$
Newform subspaces $2$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 171.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(171, [\chi])\).

Total New Old
Modular forms 124 108 16
Cusp forms 116 108 8
Eisenstein series 8 0 8

Trace form

\( 108 q + 4 q^{3} - 216 q^{4} + 28 q^{5} + 14 q^{6} - 12 q^{8} - 124 q^{9} + 80 q^{11} + 330 q^{12} + 38 q^{14} + 88 q^{15} - 864 q^{16} - 272 q^{17} - 144 q^{18} + 368 q^{20} - 40 q^{21} - 40 q^{23} + 300 q^{24}+ \cdots - 448 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.4.e.a 171.e 9.c $54$ $10.089$ None 171.4.e.a \(-6\) \(2\) \(-26\) \(0\) $\mathrm{SU}(2)[C_{3}]$
171.4.e.b 171.e 9.c $54$ $10.089$ None 171.4.e.b \(6\) \(2\) \(54\) \(0\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(171, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)