Space of modular forms of level 5, weight 34, and Character 5.b

• Label: 5.34.b
• Level: $5$
• Weight: $34$
• Character orbit: 5.b
• Rep. character: $\chi_{5}(4,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $17$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(17\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(5, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	16	16	0
Eisenstein series	2	2	0

Trace form

\( 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27535156574590368 q^{9} + O(q^{10}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(5, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.34.b.a	$5$	$34$	5.b	5.b	$2$	$16$	$16$	$34.491$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-232168160280\)	\(0\)	$2^{83}\cdot 3^{26}\cdot 5^{53}\cdot 7^{4}\cdot 11^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-52\beta _{1}+\beta _{3})q^{3}+(-4553207930+\cdots)q^{4}+\cdots\)