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Properties

Label 54.3.d
Level $54$
Weight $3$
Character orbit 54.d
Rep. character $\chi_{54}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $27$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 54.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(54, [\chi])\).

Total New Old
Modular forms 48 4 44
Cusp forms 24 4 20
Eisenstein series 24 0 24

Trace form

\( 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7} + O(q^{10}) \) \( 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7} - 18 q^{11} - 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 36 q^{20} - 12 q^{22} - 18 q^{23} + 4 q^{25} + 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} + 128 q^{37} + 72 q^{38} + 126 q^{41} - 46 q^{43} - 24 q^{46} - 54 q^{47} - 12 q^{49} + 20 q^{52} - 108 q^{55} - 72 q^{56} + 24 q^{58} - 126 q^{59} + 62 q^{61} - 32 q^{64} - 90 q^{65} - 106 q^{67} - 72 q^{68} - 108 q^{70} - 208 q^{73} - 72 q^{74} - 40 q^{76} + 90 q^{77} + 14 q^{79} + 144 q^{82} + 378 q^{83} + 108 q^{85} + 108 q^{86} + 24 q^{88} + 412 q^{91} - 36 q^{92} + 84 q^{94} - 180 q^{95} + 14 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.3.d.a $4$ $1.471$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(18\) \(2\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(6-3\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)