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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.3.b.a 38.b 19.b $2$ $1.035$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-2\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+2\beta q^{3}-2q^{4}-q^{5}-4q^{6}+\cdots\)

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

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