Properties

Label 378.2.w
Level 378
Weight 2
Character orbit w
Rep. character \(\chi_{378}(25,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 144
Newform subspaces 2
Sturm bound 144
Trace bound 7

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Defining parameters

Level: \( N \) = \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 378.w (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(378, [\chi])\).

Total New Old
Modular forms 456 144 312
Cusp forms 408 144 264
Eisenstein series 48 0 48

Trace form

\( 144q + 6q^{6} - 12q^{9} + O(q^{10}) \) \( 144q + 6q^{6} - 12q^{9} - 12q^{11} - 6q^{14} - 12q^{15} + 48q^{17} + 6q^{21} + 6q^{23} - 36q^{26} + 6q^{29} + 18q^{30} - 36q^{33} + 18q^{35} + 6q^{36} + 54q^{39} - 12q^{41} - 24q^{42} - 12q^{45} + 18q^{47} - 18q^{49} + 12q^{50} + 18q^{51} - 30q^{53} + 18q^{54} + 12q^{56} - 6q^{57} + 30q^{59} - 36q^{60} - 36q^{61} - 48q^{62} - 60q^{63} - 72q^{64} - 108q^{65} - 72q^{66} - 36q^{68} - 60q^{69} - 18q^{70} + 24q^{71} - 12q^{72} - 36q^{73} + 18q^{74} - 6q^{75} - 102q^{77} + 36q^{78} - 36q^{79} - 12q^{80} - 24q^{81} - 6q^{84} + 72q^{85} - 24q^{86} - 66q^{87} + 144q^{89} - 18q^{91} + 42q^{92} + 12q^{93} - 36q^{94} + 114q^{95} + 12q^{98} + 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(378, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
378.2.w.a \(72\) \(3.018\) None \(0\) \(0\) \(0\) \(-3\)
378.2.w.b \(72\) \(3.018\) None \(0\) \(0\) \(0\) \(3\)

Decomposition of \(S_{2}^{\mathrm{old}}(378, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database