Properties

Label 27.3.f
Level 27
Weight 3
Character orbit f
Rep. character \(\chi_{27}(2,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 30
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 27.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(27, [\chi])\).

Total New Old
Modular forms 42 42 0
Cusp forms 30 30 0
Eisenstein series 12 12 0

Trace form

\( 30q - 6q^{2} - 6q^{3} - 6q^{4} - 15q^{5} - 18q^{6} - 6q^{7} - 9q^{8} + O(q^{10}) \) \( 30q - 6q^{2} - 6q^{3} - 6q^{4} - 15q^{5} - 18q^{6} - 6q^{7} - 9q^{8} - 3q^{10} - 6q^{11} - 15q^{12} - 6q^{13} - 15q^{14} - 9q^{15} - 18q^{16} - 9q^{17} + 63q^{18} - 3q^{19} + 213q^{20} + 132q^{21} - 42q^{22} + 120q^{23} + 144q^{24} - 15q^{25} - 90q^{27} - 12q^{28} - 168q^{29} - 243q^{30} + 39q^{31} - 360q^{32} - 207q^{33} + 54q^{34} - 252q^{35} - 360q^{36} - 3q^{37} - 84q^{38} + 15q^{39} - 33q^{40} + 228q^{41} + 486q^{42} - 96q^{43} + 639q^{44} + 477q^{45} - 3q^{46} + 399q^{47} + 453q^{48} - 78q^{49} + 303q^{50} + 36q^{51} - 9q^{52} - 54q^{54} - 12q^{55} - 393q^{56} - 192q^{57} + 129q^{58} - 474q^{59} - 846q^{60} + 138q^{61} - 900q^{62} - 585q^{63} - 51q^{64} - 411q^{65} - 423q^{66} + 354q^{67} + 99q^{68} + 99q^{69} + 489q^{70} + 315q^{71} + 720q^{72} - 66q^{73} + 321q^{74} + 255q^{75} + 258q^{76} + 201q^{77} + 180q^{78} + 30q^{79} + 36q^{81} - 12q^{82} - 33q^{83} - 588q^{84} - 261q^{85} - 258q^{86} - 279q^{87} - 642q^{88} + 72q^{89} + 288q^{90} + 96q^{91} - 3q^{92} + 591q^{93} - 861q^{94} + 681q^{95} + 270q^{96} - 582q^{97} + 882q^{98} + 513q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
27.3.f.a \(30\) \(0.736\) None \(-6\) \(-6\) \(-15\) \(-6\)