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Properties

Label 54.7.d
Level $54$
Weight $7$
Character orbit 54.d
Rep. character $\chi_{54}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $63$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 7 \)
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: \(63\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(54, [\chi])\).

Total New Old
Modular forms 120 12 108
Cusp forms 96 12 84
Eisenstein series 24 0 24

Trace form

\( 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7} + O(q^{10}) \) \( 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7} - 378 q^{11} + 1680 q^{13} + 4752 q^{14} - 6144 q^{16} - 2820 q^{19} - 13824 q^{20} - 3600 q^{22} + 76248 q^{23} + 8094 q^{25} + 15360 q^{28} - 97092 q^{29} + 21480 q^{31} - 27360 q^{34} - 25536 q^{37} - 97632 q^{38} + 410562 q^{41} + 71430 q^{43} - 135072 q^{46} - 347652 q^{47} - 135954 q^{49} - 311040 q^{50} - 53760 q^{52} + 580392 q^{55} + 152064 q^{56} + 159264 q^{58} - 369738 q^{59} + 135744 q^{61} - 393216 q^{64} + 753840 q^{65} - 289938 q^{67} - 744768 q^{68} + 155952 q^{70} - 977700 q^{73} + 2197152 q^{74} - 45120 q^{76} + 159192 q^{77} - 764796 q^{79} + 1073088 q^{82} - 396900 q^{83} + 1619568 q^{85} - 3264624 q^{86} + 115200 q^{88} + 355584 q^{91} + 2439936 q^{92} - 736848 q^{94} + 2089260 q^{95} - 38874 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.7.d.a 54.d 9.d $12$ $12.423$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-432\) \(240\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-2^{5}\beta _{2}q^{4}+(-48-24\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)