Properties

Label 378.2.v
Level 378
Weight 2
Character orbit v
Rep. character \(\chi_{378}(67,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 144
Newforms 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.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Newforms: \( 2 \)
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

\(144q \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(144q \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut -\mathstrut 24q^{17} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 42q^{23} \) \(\mathstrut -\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 18q^{30} \) \(\mathstrut -\mathstrut 36q^{33} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 6q^{36} \) \(\mathstrut -\mathstrut 72q^{39} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut +\mathstrut 48q^{42} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 36q^{49} \) \(\mathstrut +\mathstrut 12q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 36q^{54} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 60q^{59} \) \(\mathstrut +\mathstrut 18q^{60} \) \(\mathstrut +\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut -\mathstrut 72q^{64} \) \(\mathstrut +\mathstrut 54q^{65} \) \(\mathstrut +\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 18q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 72q^{73} \) \(\mathstrut -\mathstrut 36q^{74} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 30q^{77} \) \(\mathstrut +\mathstrut 36q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut +\mathstrut 48q^{81} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 156q^{87} \) \(\mathstrut -\mathstrut 72q^{89} \) \(\mathstrut +\mathstrut 36q^{91} \) \(\mathstrut +\mathstrut 42q^{92} \) \(\mathstrut -\mathstrut 96q^{93} \) \(\mathstrut -\mathstrut 36q^{94} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(378, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
378.2.v.a \(72\) \(3.018\) None \(0\) \(0\) \(0\) \(-6\)
378.2.v.b \(72\) \(3.018\) None \(0\) \(0\) \(0\) \(6\)

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

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