Properties

Label 378.2.bf
Level 378
Weight 2
Character orbit bf
Rep. character \(\chi_{378}(5,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 144
Newform subspaces 1
Sturm bound 144
Trace bound 0

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Defining parameters

Level: \( N \) = \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 378.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

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

\( 144q + 18q^{6} - 12q^{9} + O(q^{10}) \) \( 144q + 18q^{6} - 12q^{9} + 12q^{11} + 6q^{14} + 12q^{15} + 6q^{21} - 6q^{23} - 6q^{29} - 18q^{30} - 54q^{35} + 6q^{36} - 6q^{39} + 24q^{42} - 54q^{47} + 18q^{49} + 12q^{50} + 18q^{51} + 90q^{53} - 54q^{54} - 12q^{56} - 6q^{57} - 90q^{59} - 36q^{60} - 24q^{63} + 72q^{64} - 84q^{65} - 36q^{69} - 18q^{70} - 72q^{71} + 12q^{72} + 18q^{74} - 90q^{75} - 78q^{77} - 60q^{78} + 36q^{79} - 6q^{84} - 72q^{85} + 24q^{86} + 90q^{87} - 18q^{91} - 42q^{92} - 12q^{93} + 78q^{95} - 36q^{98} - 108q^{99} + O(q^{100}) \)

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.bf.a \(144\) \(3.018\) None \(0\) \(0\) \(0\) \(0\)

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