Properties

Label 57.2.i
Level $57$
Weight $2$
Character orbit 57.i
Rep. character $\chi_{57}(4,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $18$
Newform subspaces $2$
Sturm bound $13$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 57.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(13\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(57, [\chi])\).

Total New Old
Modular forms 54 18 36
Cusp forms 30 18 12
Eisenstein series 24 0 24

Trace form

\( 18 q - 6 q^{4} - 6 q^{6} - 6 q^{7} - 24 q^{10} - 6 q^{11} - 6 q^{12} - 9 q^{13} + 6 q^{14} + 12 q^{15} + 18 q^{16} + 9 q^{19} - 12 q^{20} + 3 q^{21} - 24 q^{22} + 24 q^{24} - 12 q^{25} + 12 q^{26} - 3 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.2.i.a 57.i 19.e $6$ $0.455$ \(\Q(\zeta_{18})\) None 57.2.i.a \(3\) \(0\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}-\zeta_{18}^{4}q^{3}+\cdots\)
57.2.i.b 57.i 19.e $12$ $0.455$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 57.2.i.b \(-3\) \(0\) \(6\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{6}q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(57, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)