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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

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

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.d.a 38.d 19.d $4$ $1.035$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(6\) \(2\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)

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

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