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Properties

Label 54.6.c
Level $54$
Weight $6$
Character orbit 54.c
Rep. character $\chi_{54}(19,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $2$
Sturm bound $54$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 54.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(54, [\chi])\).

Total New Old
Modular forms 102 10 92
Cusp forms 78 10 68
Eisenstein series 24 0 24

Trace form

\( 10 q + 4 q^{2} - 80 q^{4} + 108 q^{5} - 58 q^{7} - 128 q^{8} + O(q^{10}) \) \( 10 q + 4 q^{2} - 80 q^{4} + 108 q^{5} - 58 q^{7} - 128 q^{8} + 393 q^{11} + 362 q^{13} + 824 q^{14} - 1280 q^{16} - 3882 q^{17} - 1018 q^{19} + 1728 q^{20} - 948 q^{22} + 8706 q^{23} + 181 q^{25} - 14800 q^{26} + 1856 q^{28} + 9042 q^{29} - 3892 q^{31} + 1024 q^{32} - 3828 q^{34} - 432 q^{35} + 30344 q^{37} + 11084 q^{38} - 20403 q^{41} + 1469 q^{43} - 12576 q^{44} - 18960 q^{46} - 37878 q^{47} - 22413 q^{49} + 23788 q^{50} + 5792 q^{52} + 128712 q^{53} + 56160 q^{55} + 13184 q^{56} - 5016 q^{58} - 84921 q^{59} - 72916 q^{61} - 106624 q^{62} + 40960 q^{64} - 121284 q^{65} + 3767 q^{67} + 31056 q^{68} - 9936 q^{70} + 277368 q^{71} - 110842 q^{73} + 99056 q^{74} + 8144 q^{76} - 110202 q^{77} + 74276 q^{79} - 55296 q^{80} + 82440 q^{82} - 123396 q^{83} - 23112 q^{85} + 256988 q^{86} - 15168 q^{88} - 47532 q^{89} - 202712 q^{91} + 139296 q^{92} - 48120 q^{94} - 68472 q^{95} + 15983 q^{97} - 666408 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.6.c.a 54.c 9.c $4$ $8.661$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-8\) \(0\) \(54\) \(74\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\beta _{1})q^{2}-2^{4}\beta _{1}q^{4}+(3^{3}\beta _{1}+\cdots)q^{5}+\cdots\)
54.6.c.b 54.c 9.c $6$ $8.661$ 6.0.\(\cdots\).3 None \(12\) \(0\) \(54\) \(-132\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{1}q^{2}+(-2^{4}+2^{4}\beta _{1})q^{4}+(18+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)