Properties

Label 38.2.e
Level $38$
Weight $2$
Character orbit 38.e
Rep. character $\chi_{38}(5,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $6$
Newform subspaces $1$
Sturm bound $10$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(38, [\chi])\).

Total New Old
Modular forms 42 6 36
Cusp forms 18 6 12
Eisenstein series 24 0 24

Trace form

\( 6q - 3q^{3} - 3q^{6} - 6q^{7} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{3} - 3q^{6} - 6q^{7} - 3q^{8} - 3q^{9} - 6q^{11} + 12q^{13} + 12q^{14} - 6q^{15} - 12q^{17} - 6q^{18} + 18q^{19} + 12q^{20} + 24q^{21} - 12q^{23} - 3q^{24} + 6q^{26} + 3q^{27} - 6q^{28} - 18q^{29} + 6q^{31} + 3q^{33} - 12q^{34} - 12q^{35} - 3q^{36} - 12q^{37} - 9q^{38} - 12q^{39} + 3q^{41} - 12q^{42} - 6q^{43} + 6q^{45} + 30q^{47} + 6q^{48} - 15q^{49} + 3q^{50} + 21q^{51} - 6q^{52} + 24q^{53} + 9q^{54} + 18q^{55} + 12q^{56} - 24q^{57} + 24q^{58} - 3q^{59} - 6q^{60} + 6q^{61} + 18q^{62} + 12q^{63} - 3q^{64} + 12q^{65} + 3q^{66} - 9q^{67} - 3q^{68} - 6q^{69} - 12q^{70} - 18q^{71} + 6q^{72} - 30q^{73} - 18q^{74} - 6q^{76} - 12q^{77} - 18q^{78} + 6q^{79} - 33q^{81} + 3q^{82} - 6q^{83} + 6q^{84} - 24q^{85} + 12q^{86} + 18q^{87} - 6q^{88} + 12q^{90} - 12q^{91} + 6q^{92} + 6q^{93} - 12q^{94} + 3q^{97} + 21q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.2.e.a \(6\) \(0.303\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(-6\) \(q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

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