Space of modular forms of level 38, weight 5, and Character 38.b

• Label: 38.5.b
• Level: $38$
• Weight: $5$
• Character orbit: 38.b
• Rep. character: $\chi_{38}(37,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $25$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	38.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
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	22	8	14
Cusp forms	18	8	10
Eisenstein series	4	0	4

Trace form

\( 8 q - 64 q^{4} + 18 q^{5} - 32 q^{6} - 162 q^{7} - 268 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
38.5.b.a	$38$	$5$	38.b	19.b	$2$	$8$	$8$	$3.928$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(-162\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-8q^{4}+(2-\beta _{6}+\cdots)q^{5}+\cdots\)

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

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