Properties

Label 54.9.d
Level $54$
Weight $9$
Character orbit 54.d
Rep. character $\chi_{54}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $81$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
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: \(81\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(54, [\chi])\).

Total New Old
Modular forms 156 16 140
Cusp forms 132 16 116
Eisenstein series 24 0 24

Trace form

\( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} + O(q^{10}) \) \( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29} + 542438 q^{31} + 220416 q^{34} + 3343328 q^{37} + 1314432 q^{38} - 9218592 q^{41} + 339512 q^{43} + 7417344 q^{46} + 34980606 q^{47} - 2364654 q^{49} - 27744768 q^{50} + 431360 q^{52} - 4584276 q^{55} + 12091392 q^{56} - 7852800 q^{58} - 93924216 q^{59} - 841954 q^{61} - 33554432 q^{64} + 126568134 q^{65} + 29946644 q^{67} + 5476608 q^{68} - 34359552 q^{70} - 7547764 q^{73} - 35124480 q^{74} + 23179520 q^{76} - 9309294 q^{77} + 33813002 q^{79} - 137346048 q^{82} - 114200226 q^{83} - 125696772 q^{85} + 171379584 q^{86} + 7913472 q^{88} + 268578316 q^{91} - 167825664 q^{92} - 11832576 q^{94} + 143949240 q^{95} - 89415484 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.9.d.a 54.d 9.d $16$ $21.998$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 18.9.d.a \(0\) \(0\) \(882\) \(-1846\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}-2^{7}\beta _{1}q^{4}+(74+37\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

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