Properties

Label 380.2.l
Level $380$
Weight $2$
Character orbit 380.l
Rep. character $\chi_{380}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
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 132 20 112
Cusp forms 108 20 88
Eisenstein series 24 0 24

Trace form

\( 20q + 2q^{5} - 2q^{7} + O(q^{10}) \) \( 20q + 2q^{5} - 2q^{7} + 8q^{11} + 10q^{17} + 20q^{23} + 14q^{25} + 14q^{35} - 26q^{43} - 40q^{45} - 6q^{47} - 16q^{55} + 24q^{57} + 16q^{61} + 2q^{63} - 54q^{73} + 10q^{77} - 68q^{81} + 20q^{83} - 52q^{85} - 80q^{87} + 8q^{93} + 22q^{95} + O(q^{100}) \)

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.l.a \(8\) \(3.034\) 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-2\) \(-6\) \(q+\beta _{6}q^{5}+(-1+\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
380.2.l.b \(12\) \(3.034\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(4\) \(4\) \(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{8})q^{5}+\beta _{6}q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)