Space of modular forms of level 136, weight 3, and Character 136.e

• Label: 136.3.e
• Level: $136$
• Weight: $3$
• Character orbit: 136.e
• Rep. character: $\chi_{136}(67,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $4$
• Sturm bound: $54$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(54\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(136, [\chi])\).

	Total	New	Old
Modular forms	38	38	0
Cusp forms	34	34	0
Eisenstein series	4	4	0

Trace form

\( 34 q - 2 q^{2} - 6 q^{4} - 2 q^{8} - 94 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(136, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
136.3.e.a	$136$	$3$	136.e	136.e	$2$	$2$	$2$	$3.706$	\(\Q(\sqrt{17}) \)	\(\Q(\sqrt{-34}) \)	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+4q^{4}+\beta q^{5}-\beta q^{7}-8q^{8}+\cdots\)
136.3.e.b	$136$	$3$	136.e	136.e	$2$	$2$	$2$	$3.706$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}+8q^{8}+\cdots\)
136.3.e.c	$136$	$3$	136.e	136.e	$2$	$2$	$2$	$3.706$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-34}) \)	✓	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+4q^{4}+\beta q^{5}-2\beta q^{7}+8q^{8}+\cdots\)
136.3.e.d	$136$	$3$	136.e	136.e	$2$	$28$	$28$	$3.706$		None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$