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Properties

Label 57.4.j
Level $57$
Weight $4$
Character orbit 57.j
Rep. character $\chi_{57}(2,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
Newform subspaces $1$
Sturm bound $26$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 57.j (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(26\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(57, [\chi])\).

Total New Old
Modular forms 132 132 0
Cusp forms 108 108 0
Eisenstein series 24 24 0

Trace form

\( 108 q - 9 q^{3} + 6 q^{4} - 36 q^{6} - 6 q^{7} - 51 q^{9} + 78 q^{10} - 9 q^{12} + 210 q^{13} - 54 q^{16} - 654 q^{19} + 75 q^{21} - 492 q^{22} - 282 q^{24} + 168 q^{25} + 648 q^{27} + 1260 q^{28} + 276 q^{30}+ \cdots - 11121 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.4.j.a 57.j 57.j $108$ $3.363$ None 57.4.j.a \(0\) \(-9\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$