Properties

Label 380.2.bj
Level $380$
Weight $2$
Character orbit 380.bj
Rep. character $\chi_{380}(23,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $672$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.bj (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 768 768 0
Cusp forms 672 672 0
Eisenstein series 96 96 0

Trace form

\( 672q - 12q^{2} - 24q^{5} - 36q^{6} - 6q^{8} + O(q^{10}) \) \( 672q - 12q^{2} - 24q^{5} - 36q^{6} - 6q^{8} - 12q^{10} - 6q^{12} - 24q^{13} - 36q^{16} - 24q^{17} - 24q^{18} + 36q^{20} - 48q^{21} - 24q^{22} - 24q^{25} - 60q^{26} - 24q^{28} - 6q^{30} + 18q^{32} - 60q^{33} + 24q^{36} - 48q^{37} - 114q^{38} - 42q^{40} - 24q^{41} - 48q^{42} - 12q^{45} - 12q^{46} - 96q^{48} - 6q^{50} - 12q^{52} - 24q^{53} - 48q^{56} - 24q^{57} + 120q^{58} - 12q^{60} - 48q^{61} + 36q^{62} - 12q^{65} - 96q^{66} - 6q^{68} - 12q^{70} + 120q^{72} - 24q^{73} - 96q^{76} - 360q^{77} - 126q^{78} + 48q^{80} - 48q^{81} + 228q^{82} - 24q^{85} - 132q^{86} - 102q^{88} + 78q^{90} + 108q^{92} - 60q^{93} - 144q^{96} - 24q^{97} + 18q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
380.2.bj.a \(672\) \(3.034\) None \(-12\) \(0\) \(-24\) \(0\)