Space of modular forms of level 38, weight 2, and Character 38.e

• 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: $0$

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

\( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
38.2.e.a	$38$	$2$	38.e	19.e	$9$	$6$	$1$	$0.303$	\(\Q(\zeta_{18})\)	None		✓	✓	✓	38.2.e.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots\)

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

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