Properties

Label 380.2.f
Level $380$
Weight $2$
Character orbit 380.f
Rep. character $\chi_{380}(151,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $2$
Sturm bound $120$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(5\)
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 40 24
Cusp forms 56 40 16
Eisenstein series 8 0 8

Trace form

\( 40q + 4q^{4} - 4q^{6} + 32q^{9} + O(q^{10}) \) \( 40q + 4q^{4} - 4q^{6} + 32q^{9} + 4q^{16} + 8q^{17} - 12q^{24} + 40q^{25} - 12q^{26} - 20q^{28} + 8q^{30} - 16q^{36} - 20q^{38} - 84q^{42} + 16q^{44} - 68q^{54} - 40q^{57} + 60q^{58} - 64q^{61} + 8q^{62} + 28q^{64} + 88q^{66} - 4q^{68} - 72q^{73} - 72q^{74} + 8q^{76} + 16q^{77} + 8q^{80} + 56q^{81} + 72q^{82} - 32q^{85} + 28q^{92} - 16q^{93} - 76q^{96} + O(q^{100}) \)

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.f.a \(20\) \(3.034\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-20\) \(0\) \(q-\beta _{12}q^{2}+\beta _{10}q^{3}+\beta _{16}q^{4}-q^{5}+\cdots\)
380.2.f.b \(20\) \(3.034\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(20\) \(0\) \(q-\beta _{15}q^{2}+\beta _{9}q^{3}-\beta _{19}q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)