Space of modular forms of level 136, weight 4, and Character 136.h

• Label: 136.4.h
• Level: $136$
• Weight: $4$
• Character orbit: 136.h
• Rep. character: $\chi_{136}(101,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(136, [\chi])\).

	Total	New	Old
Modular forms	56	56	0
Cusp forms	52	52	0
Eisenstein series	4	4	0

Trace form

\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(136, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
136.4.h.a	$136$	$4$	136.h	136.h	$2$	$52$	$52$	$8.024$		None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$