Space of modular forms of level 136, weight 2, and Character 136.h

• Label: 136.2.h
• Level: $136$
• Weight: $2$
• Character orbit: 136.h
• Rep. character: $\chi_{136}(101,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(136, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

\( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(136, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
136.2.h.a	$136$	$2$	136.h	136.h	$2$	$16$	$16$	$1.086$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{12}q^{3}-\beta _{3}q^{4}-\beta _{6}q^{5}+\cdots\)