Properties

Label 378.2.z
Level 378
Weight 2
Character orbit z
Rep. character \(\chi_{378}(41,\cdot)\)
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.z (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

\( 144q - 12q^{9} + O(q^{10}) \) \( 144q - 12q^{9} + 12q^{11} + 6q^{14} + 12q^{15} + 24q^{21} - 60q^{23} + 12q^{29} - 72q^{30} + 54q^{35} - 12q^{36} + 48q^{39} + 24q^{42} + 18q^{49} - 60q^{50} - 36q^{51} + 6q^{56} - 60q^{57} - 36q^{60} - 78q^{63} + 72q^{64} - 120q^{65} + 36q^{70} - 72q^{71} - 24q^{72} - 36q^{74} + 66q^{77} - 60q^{78} - 72q^{79} + 12q^{84} - 72q^{85} - 48q^{86} - 18q^{91} + 12q^{92} + 24q^{93} - 120q^{95} + 36q^{98} + 144q^{99} + O(q^{100}) \)

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

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

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