Properties

Label 38.4.e
Level $38$
Weight $4$
Character orbit 38.e
Rep. character $\chi_{38}(5,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $30$
Newform subspaces $2$
Sturm bound $20$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(38, [\chi])\).

Total New Old
Modular forms 102 30 72
Cusp forms 78 30 48
Eisenstein series 24 0 24

Trace form

\( 30q - 3q^{3} - 30q^{6} - 12q^{7} + 24q^{8} + 15q^{9} + O(q^{10}) \) \( 30q - 3q^{3} - 30q^{6} - 12q^{7} + 24q^{8} + 15q^{9} - 84q^{11} + 72q^{12} + 138q^{13} + 24q^{14} + 240q^{15} - 42q^{17} - 276q^{18} - 834q^{19} - 192q^{20} - 486q^{21} + 24q^{22} + 132q^{23} - 120q^{24} + 876q^{25} + 228q^{26} + 867q^{27} + 408q^{28} + 828q^{29} + 30q^{31} - 1245q^{33} + 360q^{34} - 2130q^{35} + 60q^{36} + 60q^{37} - 474q^{38} + 564q^{39} - 63q^{41} + 72q^{42} - 516q^{43} + 768q^{44} + 2790q^{45} + 1200q^{46} + 1932q^{47} + 96q^{48} + 555q^{49} + 714q^{50} + 345q^{51} - 816q^{52} - 882q^{53} - 3438q^{54} - 1296q^{55} - 864q^{56} - 5484q^{57} - 1296q^{58} - 4197q^{59} + 240q^{60} - 990q^{61} - 1764q^{62} + 1578q^{63} - 960q^{64} + 2250q^{65} + 3162q^{66} + 2385q^{67} - 540q^{68} + 3456q^{69} + 3720q^{70} + 4650q^{71} + 1104q^{72} - 378q^{73} - 396q^{74} - 6300q^{75} - 408q^{76} + 4404q^{77} + 4884q^{78} + 216q^{79} + 5205q^{81} + 714q^{82} + 1308q^{83} + 1296q^{84} - 2028q^{85} - 2208q^{86} - 1614q^{87} + 528q^{88} - 1980q^{89} - 7224q^{90} - 516q^{91} - 2784q^{92} - 7734q^{93} + 168q^{94} + 1434q^{95} - 453q^{97} - 576q^{98} - 561q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.4.e.a \(12\) \(2.242\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-9\) \(0\) \(21\) \(q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots\)
38.4.e.b \(18\) \(2.242\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(6\) \(0\) \(-33\) \(q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)