Properties

Label 54.3.f
Level 54
Weight 3
Character orbit f
Rep. character \(\chi_{54}(5,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 36
Newform subspaces 1
Sturm bound 27
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 54.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(54, [\chi])\).

Total New Old
Modular forms 120 36 84
Cusp forms 96 36 60
Eisenstein series 24 0 24

Trace form

\( 36q + 18q^{5} + 12q^{6} - 12q^{9} + O(q^{10}) \) \( 36q + 18q^{5} + 12q^{6} - 12q^{9} - 18q^{11} - 12q^{12} - 36q^{14} - 18q^{15} - 48q^{18} - 72q^{20} - 228q^{21} + 36q^{22} - 180q^{23} + 18q^{25} + 54q^{27} + 144q^{29} + 144q^{30} - 90q^{31} + 324q^{33} - 72q^{34} + 486q^{35} + 168q^{36} + 180q^{38} + 102q^{39} - 90q^{41} + 48q^{42} + 90q^{43} - 378q^{45} - 378q^{47} - 24q^{48} + 72q^{49} - 54q^{51} - 36q^{54} - 72q^{56} + 72q^{57} + 252q^{59} + 36q^{60} - 144q^{61} + 318q^{63} + 144q^{64} + 18q^{65} - 432q^{66} - 594q^{67} - 180q^{68} - 522q^{69} - 360q^{70} - 648q^{71} - 192q^{72} + 126q^{73} - 504q^{74} - 438q^{75} - 72q^{76} - 342q^{77} - 288q^{78} - 72q^{79} + 324q^{81} + 594q^{83} + 216q^{84} + 360q^{85} + 540q^{86} + 1062q^{87} + 144q^{88} + 648q^{89} + 720q^{90} - 198q^{91} + 396q^{92} + 462q^{93} + 504q^{94} + 252q^{95} + 96q^{96} + 702q^{97} + 648q^{98} + 126q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
54.3.f.a \(36\) \(1.471\) None \(0\) \(0\) \(18\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database