Properties

Label 38.3.d
Level $38$
Weight $3$
Character orbit 38.d
Rep. character $\chi_{38}(27,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
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 24 4 20
Cusp forms 16 4 12
Eisenstein series 8 0 8

Trace form

\( 4q + 6q^{3} + 4q^{4} + 2q^{5} - 4q^{6} + 8q^{7} - 8q^{9} + O(q^{10}) \) \( 4q + 6q^{3} + 4q^{4} + 2q^{5} - 4q^{6} + 8q^{7} - 8q^{9} - 40q^{11} - 30q^{13} - 24q^{14} + 6q^{15} - 8q^{16} + 14q^{17} + 16q^{19} + 8q^{20} + 36q^{21} + 24q^{22} - 10q^{23} + 8q^{24} + 48q^{25} + 48q^{26} + 8q^{28} + 66q^{29} - 8q^{30} - 84q^{33} + 24q^{34} + 4q^{35} + 16q^{36} - 84q^{38} - 108q^{39} + 18q^{41} - 32q^{42} + 38q^{43} - 40q^{44} - 16q^{45} - 70q^{47} - 24q^{48} - 84q^{49} + 18q^{51} - 60q^{52} - 42q^{53} - 28q^{54} - 20q^{55} + 102q^{57} + 144q^{58} + 42q^{59} + 12q^{60} + 74q^{61} + 32q^{63} - 32q^{64} + 64q^{66} + 102q^{67} + 56q^{68} - 24q^{70} + 306q^{71} + 48q^{72} + 98q^{73} + 72q^{74} + 4q^{76} - 176q^{77} + 132q^{78} - 126q^{79} + 8q^{80} + 10q^{81} - 168q^{82} - 64q^{83} - 14q^{85} - 276q^{86} - 12q^{87} - 6q^{89} - 24q^{90} - 204q^{91} + 20q^{92} - 108q^{93} + 14q^{95} + 32q^{96} - 486q^{97} - 96q^{98} + 32q^{99} + O(q^{100}) \)

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.d.a \(4\) \(1.035\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(6\) \(2\) \(8\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)

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

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