Space of modular forms of level 136, weight 4, and Character 136.n

• Label: 136.4.n
• Level: $136$
• Weight: $4$
• Character orbit: 136.n
• Rep. character: $\chi_{136}(9,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $52$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.n (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(136, [\chi])\).

	Total	New	Old
Modular forms	232	52	180
Cusp forms	200	52	148
Eisenstein series	32	0	32

Trace form

52 * q + 60 * q^9 + 100 * q^11 - 8 * q^17 - 456 * q^25 - 660 * q^27 - 296 * q^29 + 432 * q^31 + 1024 * q^33 + 2176 * q^35 + 768 * q^37 + 48 * q^39 - 584 * q^41 - 1308 * q^43 - 720 * q^45 + 760 * q^49 + 192 * q^53 - 1152 * q^57 - 524 * q^59 - 600 * q^61 - 2496 * q^63 + 16 * q^65 - 1464 * q^67 - 5328 * q^69 - 1320 * q^71 + 1608 * q^73 - 92 * q^75 + 2304 * q^77 + 872 * q^79 + 3188 * q^83 - 3648 * q^85 + 2496 * q^87 + 1392 * q^91 + 3664 * q^93 - 552 * q^95 + 1188 * q^97 - 1416 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(136, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
136.4.n.a	$136$	$4$	136.n	17.d	$8$	$24$	$6$	$8.024$		None		✓			136.4.n.a	$2$	$0$	\(0\)	\(0\)	\(-28\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
136.4.n.b	$136$	$4$	136.n	17.d	$8$	$28$	$7$	$8.024$		None		✓	✓		136.4.n.b	$2$	$0$	\(0\)	\(0\)	\(28\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{4}^{\mathrm{old}}(136, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(136, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)