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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.bb.a 380.bb 380.ab $336$ $3.034$ None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$