Properties

Label 38.3.b
Level $38$
Weight $3$
Character orbit 38.b
Rep. character $\chi_{38}(37,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 38.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(38, [\chi])\).

Total New Old
Modular forms 12 2 10
Cusp forms 8 2 6
Eisenstein series 4 0 4

Trace form

\( 2q - 4q^{4} - 2q^{5} - 8q^{6} + 10q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - 4q^{4} - 2q^{5} - 8q^{6} + 10q^{7} + 2q^{9} + 10q^{11} + 8q^{16} - 50q^{17} + 38q^{19} + 4q^{20} - 20q^{23} + 16q^{24} - 48q^{25} + 48q^{26} - 20q^{28} + 8q^{30} - 10q^{35} - 4q^{36} + 96q^{39} - 40q^{42} + 10q^{43} - 20q^{44} - 2q^{45} + 10q^{47} - 48q^{49} - 80q^{54} - 10q^{55} - 120q^{58} + 190q^{61} + 120q^{62} + 10q^{63} - 16q^{64} - 40q^{66} + 100q^{68} - 50q^{73} + 72q^{74} - 76q^{76} + 50q^{77} - 8q^{80} - 142q^{81} + 120q^{82} - 260q^{83} + 50q^{85} - 240q^{87} + 40q^{92} + 240q^{93} - 38q^{95} - 32q^{96} + 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.3.b.a \(2\) \(1.035\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-2\) \(10\) \(q+\beta q^{2}+2\beta q^{3}-2q^{4}-q^{5}-4q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)