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

• Label: 136.2.o
• Level: $136$
• Weight: $2$
• Character orbit: 136.o
• Rep. character: $\chi_{136}(53,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $64$
• 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.o (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{8})\)
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	80	80	0
Cusp forms	64	64	0
Eisenstein series	16	16	0

Trace form

64 * q - 4 * q^2 - 12 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 20 * q^20 + 20 * q^22 - 8 * q^23 + 8 * q^24 + 4 * q^26 - 12 * q^28 - 8 * q^31 - 44 * q^32 - 16 * q^33 + 28 * q^34 - 20 * q^36 - 32 * q^39 - 64 * q^40 + 32 * q^42 - 36 * q^44 + 36 * q^46 + 60 * q^48 - 8 * q^49 - 48 * q^50 - 40 * q^52 + 60 * q^54 + 44 * q^56 + 8 * q^57 - 8 * q^58 + 56 * q^60 + 4 * q^62 - 32 * q^63 - 88 * q^65 + 100 * q^66 + 76 * q^68 + 16 * q^70 + 56 * q^71 + 32 * q^73 + 76 * q^74 + 40 * q^76 + 48 * q^78 - 8 * q^79 + 88 * q^80 - 32 * q^82 - 48 * q^84 - 16 * q^86 - 8 * q^87 + 72 * q^88 - 132 * q^90 + 28 * q^92 - 24 * q^94 - 8 * q^95 + 20 * q^96 - 8 * q^97

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.o.a	$136$	$2$	136.o	136.o	$8$	$64$	$16$	$1.086$		None		✓	✓	✓	136.2.o.a	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{8}]$