Properties

Label 38.5.d
Level $38$
Weight $5$
Character orbit 38.d
Rep. character $\chi_{38}(27,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
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.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
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 44 16 28
Cusp forms 36 16 20
Eisenstein series 8 0 8

Trace form

\( 16q - 12q^{3} + 64q^{4} - 18q^{5} - 16q^{6} + 72q^{7} + 352q^{9} + O(q^{10}) \) \( 16q - 12q^{3} + 64q^{4} - 18q^{5} - 16q^{6} + 72q^{7} + 352q^{9} - 84q^{11} + 450q^{13} + 288q^{14} - 390q^{15} - 512q^{16} + 606q^{17} - 306q^{19} - 288q^{20} - 2160q^{21} - 1680q^{22} - 54q^{23} + 128q^{24} - 434q^{25} + 1344q^{26} + 288q^{28} - 4914q^{29} + 2752q^{30} + 7890q^{33} - 1536q^{34} + 2328q^{35} - 2816q^{36} + 1344q^{38} + 7620q^{39} - 1692q^{41} + 2080q^{42} - 7402q^{43} - 336q^{44} - 16720q^{45} + 3198q^{47} + 768q^{48} + 24816q^{49} + 10710q^{51} + 3600q^{52} + 3870q^{53} - 16q^{54} - 13588q^{55} + 3702q^{57} - 1728q^{58} - 18288q^{59} - 3120q^{60} - 6522q^{61} - 6144q^{62} - 15676q^{63} - 8192q^{64} + 4960q^{66} - 30168q^{67} + 9696q^{68} + 15360q^{70} + 35874q^{71} + 5376q^{72} - 8080q^{73} - 9120q^{74} + 480q^{76} + 34560q^{77} - 46560q^{78} - 30738q^{79} - 1152q^{80} - 30920q^{81} + 6720q^{82} - 1476q^{83} + 33626q^{85} + 288q^{86} + 113100q^{87} + 19782q^{89} + 44256q^{90} - 34260q^{91} + 432q^{92} - 4272q^{93} - 23706q^{95} + 2048q^{96} - 9936q^{97} + 12672q^{98} + 3848q^{99} + O(q^{100}) \)

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.d.a \(16\) \(3.928\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-12\) \(-18\) \(72\) \(q+(-\beta _{5}+\beta _{9})q^{2}+(-1+\beta _{3})q^{3}+8\beta _{7}q^{4}+\cdots\)

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

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