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

• Label: 136.2.s
• Level: $136$
• Weight: $2$
• Character orbit: 136.s
• Rep. character: $\chi_{136}(3,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $128$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.s (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	160	160	0
Cusp forms	128	128	0
Eisenstein series	32	32	0

Trace form

128 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 - 8 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 + 8 * q^24 - 16 * q^25 - 40 * q^26 - 16 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 - 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 16 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 + 8 * q^54 + 32 * q^56 - 48 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 + 112 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 + 16 * q^81 + 32 * q^82 - 16 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 32 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
136.2.s.a	$136$	$2$	136.s	136.s	$16$	$8$	$1$	$1.086$	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-2}) \)		✓			136.2.s.a	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{16}]$	\(q+(-\zeta_{16}+\zeta_{16}^{5})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\)
136.2.s.b	$136$	$2$	136.s	136.s	$16$	$8$	$1$	$1.086$	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-2}) \)		✓			136.2.s.b	$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{16}]$	\(q+(\zeta_{16}-\zeta_{16}^{5})q^{2}+(1+\zeta_{16}-\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
136.2.s.c	$136$	$2$	136.s	136.s	$16$	$112$	$14$	$1.086$		None		✓	✓		136.2.s.c	$4$	$0$	\(-8\)	\(-16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$