Properties

Label 38.5.b
Level $38$
Weight $5$
Character orbit 38.b
Rep. character $\chi_{38}(37,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $25$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(25\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(38, [\chi])\).

Total New Old
Modular forms 22 8 14
Cusp forms 18 8 10
Eisenstein series 4 0 4

Trace form

\( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} + O(q^{10}) \) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} - 6q^{11} + 512q^{16} + 510q^{17} - 12q^{19} - 144q^{20} - 396q^{23} + 256q^{24} + 3458q^{25} - 192q^{26} + 1296q^{28} - 2752q^{30} + 1002q^{35} + 2144q^{36} - 3216q^{38} - 6588q^{39} + 1376q^{42} - 8654q^{43} + 48q^{44} - 10334q^{45} + 3210q^{47} + 9222q^{49} + 9088q^{54} + 17146q^{55} - 14076q^{57} - 960q^{58} + 1314q^{61} - 15168q^{62} + 29938q^{63} - 4096q^{64} + 4928q^{66} - 4080q^{68} + 23398q^{73} + 13152q^{74} + 96q^{76} - 44622q^{77} + 1152q^{80} - 20368q^{81} + 16512q^{82} - 10440q^{83} + 21274q^{85} - 14316q^{87} + 3168q^{92} + 19416q^{93} - 34686q^{95} - 2048q^{96} - 56798q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.5.b.a \(8\) \(3.928\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(18\) \(-162\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-8q^{4}+(2-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)