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

• Label: 136.3.p
• Level: $136$
• Weight: $3$
• Character orbit: 136.p
• Rep. character: $\chi_{136}(19,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $136$
• Newform subspaces: $3$
• Sturm bound: $54$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.p (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(54\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	152	152	0
Cusp forms	136	136	0
Eisenstein series	16	16	0

Trace form

\( 136 q - 4 q^{2} - 8 q^{3} - 28 q^{6} - 4 q^{8} - 8 q^{9} + O(q^{10}) \)

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.p.a	$136$	$3$	136.p	136.p	$8$	$4$	$1$	$3.706$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{8}]$	\(q-2\zeta_{8}^{3}q^{2}+(-2-2\zeta_{8}-3\zeta_{8}^{2}+3\zeta_{8}^{3})q^{3}+\cdots\)
136.3.p.b	$136$	$3$	136.p	136.p	$8$	$4$	$1$	$3.706$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{8}]$	\(q-2\zeta_{8}^{3}q^{2}+(2+2\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
136.3.p.c	$136$	$3$	136.p	136.p	$8$	$128$	$32$	$3.706$		None		$4$	$0$	\(-4\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$