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Properties

Label 54.2.c
Level $54$
Weight $2$
Character orbit 54.c
Rep. character $\chi_{54}(19,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 54.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(54, [\chi])\).

Total New Old
Modular forms 30 2 28
Cusp forms 6 2 4
Eisenstein series 24 0 24

Trace form

\( 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} + O(q^{10}) \) \( 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} - 3 q^{11} - 2 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} - 2 q^{19} + 3 q^{22} - 6 q^{23} + 5 q^{25} - 4 q^{26} + 4 q^{28} + 6 q^{29} + 4 q^{31} + q^{32} + 3 q^{34} - 8 q^{37} - q^{38} + 9 q^{41} + q^{43} + 6 q^{44} - 12 q^{46} - 6 q^{47} + 3 q^{49} - 5 q^{50} - 2 q^{52} - 24 q^{53} + 2 q^{56} - 6 q^{58} + 3 q^{59} - 8 q^{61} + 8 q^{62} + 2 q^{64} - 5 q^{67} - 3 q^{68} + 24 q^{71} + 22 q^{73} - 4 q^{74} + q^{76} - 6 q^{77} + 4 q^{79} + 18 q^{82} + 12 q^{83} - q^{86} + 3 q^{88} - 12 q^{89} + 8 q^{91} - 6 q^{92} + 6 q^{94} - 5 q^{97} + 6 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.2.c.a 54.c 9.c $2$ $0.431$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)