Space of modular forms of level 4, weight 39, and Character 4.b

• Label: 4.39.b
• Level: $4$
• Weight: $39$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $19$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 39 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(19\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{39}(4, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	18	18	0
Eisenstein series	2	2	0

Trace form

\( 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90410803724813632 q^{8} - 7529771892957713214 q^{9} + O(q^{10}) \)

Decomposition of \(S_{39}^{\mathrm{new}}(4, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.39.b.a	$4$	$39$	4.b	4.b	$2$	$18$	$18$	$36.585$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(364228\)	\(0\)	\(-89\!\cdots\!20\)	\(0\)	$2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(20235-\beta _{1})q^{2}+(-18+165\beta _{1}+\cdots)q^{3}+\cdots\)