Properties

Label 38.7.b
Level $38$
Weight $7$
Character orbit 38.b
Rep. character $\chi_{38}(37,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $1$
Sturm bound $35$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(35\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(38, [\chi])\).

Total New Old
Modular forms 32 10 22
Cusp forms 28 10 18
Eisenstein series 4 0 4

Trace form

\( 10q - 320q^{4} - 112q^{5} + 160q^{6} - 224q^{7} - 2890q^{9} + O(q^{10}) \) \( 10q - 320q^{4} - 112q^{5} + 160q^{6} - 224q^{7} - 2890q^{9} + 3644q^{11} + 10240q^{16} - 10420q^{17} - 17230q^{19} + 3584q^{20} + 37712q^{23} - 5120q^{24} - 52078q^{25} - 7104q^{26} + 7168q^{28} + 94688q^{30} - 161720q^{35} + 92480q^{36} + 25152q^{38} - 78876q^{39} + 53792q^{42} + 6308q^{43} - 116608q^{44} + 309808q^{45} + 322220q^{47} - 235770q^{49} - 321728q^{54} - 377880q^{55} + 24228q^{57} + 445920q^{58} + 426304q^{61} + 59424q^{62} - 517916q^{63} - 327680q^{64} - 1417312q^{66} + 333440q^{68} - 786076q^{73} - 293280q^{74} + 551360q^{76} + 2303716q^{77} - 114688q^{80} + 5261090q^{81} - 455136q^{82} - 101500q^{83} - 1261380q^{85} - 2460732q^{87} - 1206784q^{92} - 2827032q^{93} + 3106292q^{95} + 163840q^{96} + 1061428q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.7.b.a \(10\) \(8.742\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-112\) \(-224\) \(q-\beta _{6}q^{2}+(\beta _{5}+\beta _{6})q^{3}-2^{5}q^{4}+(-11+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)