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Properties

Label 54.5.d
Level $54$
Weight $5$
Character orbit 54.d
Rep. character $\chi_{54}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $45$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
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: \(45\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(54, [\chi])\).

Total New Old
Modular forms 84 8 76
Cusp forms 60 8 52
Eisenstein series 24 0 24

Trace form

\( 8 q + 32 q^{4} - 18 q^{5} - 26 q^{7} + O(q^{10}) \) \( 8 q + 32 q^{4} - 18 q^{5} - 26 q^{7} + 720 q^{11} + 10 q^{13} - 288 q^{14} - 256 q^{16} + 100 q^{19} - 144 q^{20} + 336 q^{22} - 1278 q^{23} + 794 q^{25} - 416 q^{28} + 1854 q^{29} - 1478 q^{31} - 96 q^{34} - 32 q^{37} - 6768 q^{38} + 36 q^{41} - 68 q^{43} + 2112 q^{46} - 2214 q^{47} + 2442 q^{49} + 15552 q^{50} - 80 q^{52} - 3996 q^{55} - 2304 q^{56} - 2400 q^{58} - 9108 q^{59} - 4478 q^{61} - 4096 q^{64} + 22554 q^{65} + 7504 q^{67} + 11088 q^{68} + 6048 q^{70} + 20716 q^{73} - 15264 q^{74} + 400 q^{76} - 34434 q^{77} - 6050 q^{79} + 1152 q^{82} + 3834 q^{83} - 16092 q^{85} + 12528 q^{86} - 2688 q^{88} - 45868 q^{91} - 10224 q^{92} + 672 q^{94} - 20880 q^{95} + 31336 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.5.d.a 54.d 9.d $8$ $5.582$ 8.0.\(\cdots\).4 None \(0\) \(0\) \(-18\) \(-26\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+8\beta _{2}q^{4}+(-3-\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)