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

• Label: 136.2.c
• Level: $136$
• Weight: $2$
• Character orbit: 136.c
• Rep. character: $\chi_{136}(69,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

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

Trace form

16 * q - 2 * q^2 + 2 * q^4 + 6 * q^6 - 4 * q^7 - 2 * q^8 - 16 * q^9 - 2 * q^10 + 14 * q^12 - 4 * q^14 + 2 * q^16 - 10 * q^18 - 2 * q^20 - 10 * q^22 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 20 * q^26 - 16 * q^28 + 16 * q^30 + 12 * q^31 - 2 * q^32 - 30 * q^36 - 12 * q^38 + 8 * q^39 + 22 * q^40 + 8 * q^42 - 6 * q^44 - 44 * q^46 - 24 * q^47 - 22 * q^48 + 2 * q^50 - 12 * q^52 + 16 * q^54 + 32 * q^55 - 12 * q^56 + 16 * q^57 + 2 * q^58 + 56 * q^60 + 36 * q^62 + 20 * q^63 + 26 * q^64 + 12 * q^66 + 40 * q^70 - 36 * q^71 - 34 * q^72 + 16 * q^73 - 46 * q^74 + 4 * q^76 + 28 * q^78 - 20 * q^79 - 50 * q^80 + 20 * q^82 + 40 * q^84 - 8 * q^86 + 32 * q^87 + 22 * q^88 + 16 * q^89 - 14 * q^90 - 12 * q^92 - 64 * q^94 + 16 * q^95 + 58 * q^96 - 66 * q^98

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.c.a	$136$	$2$	136.c	8.b	$2$	$8$	$8$	$1.086$	8.0.1649659456.5	None		✓			136.2.c.a	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
136.2.c.b	$136$	$2$	136.c	8.b	$2$	$8$	$8$	$1.086$	8.0.4469724736.1	None		✓			136.2.c.b	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)