Properties

Label 38.3.f
Level $38$
Weight $3$
Character orbit 38.f
Rep. character $\chi_{38}(3,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $24$
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.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
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 72 24 48
Cusp forms 48 24 24
Eisenstein series 24 0 24

Trace form

\( 24q - 6q^{3} + 12q^{6} - 18q^{7} + 6q^{9} + O(q^{10}) \) \( 24q - 6q^{3} + 12q^{6} - 18q^{7} + 6q^{9} + 30q^{11} - 36q^{12} - 90q^{13} - 48q^{14} - 114q^{15} + 18q^{17} - 12q^{19} + 24q^{20} + 90q^{21} + 84q^{22} + 120q^{23} - 24q^{24} + 252q^{25} + 48q^{26} + 126q^{27} + 72q^{28} - 210q^{29} - 108q^{31} - 132q^{33} - 24q^{34} - 66q^{35} - 12q^{36} + 84q^{38} + 120q^{39} + 54q^{41} + 72q^{42} + 90q^{43} - 48q^{44} - 144q^{45} - 360q^{46} - 246q^{47} - 48q^{48} + 54q^{49} - 432q^{50} - 342q^{51} + 36q^{52} - 174q^{53} - 42q^{55} - 12q^{57} + 48q^{58} + 228q^{59} + 132q^{60} + 12q^{61} + 204q^{62} + 174q^{63} + 96q^{64} + 630q^{65} + 696q^{66} + 72q^{67} - 48q^{68} + 702q^{69} + 528q^{70} + 432q^{71} + 96q^{72} - 144q^{74} + 72q^{76} - 144q^{77} - 708q^{78} - 246q^{79} - 642q^{81} - 384q^{82} - 126q^{83} - 540q^{84} - 684q^{85} - 12q^{86} - 324q^{87} - 12q^{89} - 336q^{90} + 372q^{91} - 132q^{92} - 168q^{93} - 570q^{95} + 72q^{97} + 384q^{98} - 204q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.3.f.a \(24\) \(1.035\) None \(0\) \(-6\) \(0\) \(-18\)

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

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