Properties

Label 380.2.bb
Level $380$
Weight $2$
Character orbit 380.bb
Rep. character $\chi_{380}(59,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $336$
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.bb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{18})\)
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 384 384 0
Cusp forms 336 336 0
Eisenstein series 48 48 0

Trace form

\( 336q - 18q^{4} - 12q^{5} - 18q^{6} - 24q^{9} + O(q^{10}) \) \( 336q - 18q^{4} - 12q^{5} - 18q^{6} - 24q^{9} - 15q^{10} + 18q^{14} - 6q^{16} - 42q^{20} + 12q^{21} + 12q^{24} - 12q^{25} + 18q^{26} - 24q^{29} - 24q^{30} + 12q^{34} - 6q^{36} - 48q^{40} - 12q^{41} - 36q^{44} - 6q^{45} - 18q^{46} - 108q^{49} - 36q^{50} + 36q^{54} - 30q^{60} - 24q^{61} + 18q^{64} - 18q^{65} - 48q^{66} - 180q^{69} - 21q^{70} - 30q^{74} - 48q^{76} + 3q^{80} - 60q^{81} + 90q^{84} - 36q^{85} + 102q^{86} - 48q^{89} - 78q^{90} + 24q^{96} + O(q^{100}) \)

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.bb.a \(336\) \(3.034\) None \(0\) \(0\) \(-12\) \(0\)