Properties

Label 54.4.c
Level $54$
Weight $4$
Character orbit 54.c
Rep. character $\chi_{54}(19,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(54, [\chi])\).

Total New Old
Modular forms 66 6 60
Cusp forms 42 6 36
Eisenstein series 24 0 24

Trace form

\( 6q - 2q^{2} - 12q^{4} - 18q^{5} + 12q^{7} + 16q^{8} + O(q^{10}) \) \( 6q - 2q^{2} - 12q^{4} - 18q^{5} + 12q^{7} + 16q^{8} - 39q^{11} - 24q^{13} - 100q^{14} - 48q^{16} + 78q^{17} + 210q^{19} - 72q^{20} - 18q^{22} + 264q^{23} - 219q^{25} + 392q^{26} - 96q^{28} + 348q^{29} - 6q^{31} - 32q^{32} + 90q^{34} - 1332q^{35} + 192q^{37} - 322q^{38} + 207q^{41} + 129q^{43} + 312q^{44} + 504q^{46} + 660q^{47} - 585q^{49} - 614q^{50} - 96q^{52} - 528q^{53} - 1404q^{55} - 400q^{56} + 252q^{58} + 327q^{59} + 858q^{61} + 1664q^{62} + 384q^{64} - 414q^{65} + 1587q^{67} - 156q^{68} + 216q^{70} + 312q^{71} - 258q^{73} - 856q^{74} - 420q^{76} - 708q^{77} - 1482q^{79} + 576q^{80} - 2916q^{82} + 138q^{83} + 108q^{85} + 86q^{86} - 72q^{88} + 3084q^{89} + 2508q^{91} + 1056q^{92} + 612q^{94} + 2016q^{95} + 1029q^{97} - 2604q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
54.4.c.a \(2\) \(3.186\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-9\) \(31\) \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots\)
54.4.c.b \(4\) \(3.186\) \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(-4\) \(0\) \(-9\) \(-19\) \(q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

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