Properties

Label 380.2.d
Level $380$
Weight $2$
Character orbit 380.d
Rep. character $\chi_{380}(379,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

Trace form

\( 56q - 4q^{5} + 8q^{6} - 56q^{9} + O(q^{10}) \) \( 56q - 4q^{5} + 8q^{6} - 56q^{9} - 8q^{16} - 20q^{20} - 32q^{24} - 4q^{25} - 16q^{30} - 32q^{36} + 32q^{44} - 12q^{45} + 16q^{49} - 32q^{54} + 24q^{61} + 72q^{64} + 8q^{66} + 32q^{74} + 56q^{76} - 24q^{80} + 72q^{81} + 44q^{85} + 96q^{96} + O(q^{100}) \)

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.d.a \(16\) \(3.034\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{6}q^{5}+\cdots\)
380.2.d.b \(40\) \(3.034\) None \(0\) \(0\) \(-4\) \(0\)