Properties

Label 54.5.f
Level 54
Weight 5
Character orbit f
Rep. character \(\chi_{54}(5,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 72
Newform subspaces 1
Sturm bound 45
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
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: \(45\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(54, [\chi])\).

Total New Old
Modular forms 228 72 156
Cusp forms 204 72 132
Eisenstein series 24 0 24

Trace form

\( 72q - 18q^{5} - 96q^{6} + 204q^{9} + O(q^{10}) \) \( 72q - 18q^{5} - 96q^{6} + 204q^{9} + 720q^{11} + 96q^{12} - 288q^{14} - 1422q^{15} - 1344q^{18} + 288q^{20} + 4308q^{21} - 1008q^{22} + 4716q^{23} - 882q^{25} - 2808q^{27} - 6084q^{29} - 6336q^{30} + 3330q^{31} - 1026q^{33} + 288q^{34} + 5346q^{35} + 2976q^{36} + 576q^{38} - 4974q^{39} - 13356q^{41} - 3840q^{42} + 1260q^{43} + 9558q^{45} + 16578q^{47} + 1920q^{48} - 5904q^{49} + 15552q^{50} + 20898q^{51} - 4896q^{54} - 2304q^{56} - 34218q^{57} - 40104q^{59} - 4176q^{60} + 8352q^{61} - 4110q^{63} + 18432q^{64} - 19674q^{65} - 10368q^{66} - 24192q^{67} + 10224q^{68} + 47106q^{69} + 14400q^{70} + 39528q^{71} + 15360q^{72} - 12222q^{73} + 33120q^{74} + 41682q^{75} + 9792q^{76} + 28206q^{77} - 4608q^{78} + 11304q^{79} + 6804q^{81} - 30078q^{83} - 2592q^{84} - 52200q^{85} - 46224q^{86} - 111690q^{87} - 16128q^{88} - 102222q^{89} - 66240q^{90} + 12078q^{91} - 27504q^{92} - 11958q^{93} + 4032q^{94} + 46728q^{95} + 6144q^{96} + 49680q^{97} + 82944q^{98} + 179622q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
54.5.f.a \(72\) \(5.582\) None \(0\) \(0\) \(-18\) \(0\)

Decomposition of \(S_{5}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database