Space of modular forms of level 158, weight 2, and Character 158.e

• Label: 158.2.e
• Level: $158$
• Weight: $2$
• Character orbit: 158.e
• Rep. character: $\chi_{158}(21,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	158.e (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{13})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(158, [\chi])\).

	Total	New	Old
Modular forms	264	96	168
Cusp forms	216	96	120
Eisenstein series	48	0	48

Trace form

96 * q - 2 * q^3 - 8 * q^4 - 2 * q^6 - 12 * q^7 - 20 * q^9 - 4 * q^10 - 12 * q^11 - 2 * q^12 - 12 * q^13 - 4 * q^14 + 20 * q^15 - 8 * q^16 - 20 * q^17 - 16 * q^18 - 16 * q^19 + 12 * q^21 + 22 * q^22 - 20 * q^23 + 24 * q^24 - 2 * q^25 - 8 * q^26 + 46 * q^27 - 12 * q^28 - 34 * q^29 - 24 * q^30 - 6 * q^31 - 40 * q^33 - 20 * q^34 + 34 * q^35 - 20 * q^36 + 14 * q^37 - 24 * q^38 - 12 * q^39 - 4 * q^40 - 28 * q^41 + 16 * q^42 - 34 * q^43 + 40 * q^44 - 40 * q^45 - 12 * q^46 + 16 * q^47 - 2 * q^48 - 16 * q^49 + 20 * q^50 - 32 * q^51 - 12 * q^52 - 50 * q^53 - 32 * q^54 - 84 * q^55 + 48 * q^56 - 60 * q^57 - 34 * q^58 - 18 * q^59 - 32 * q^60 - 82 * q^61 - 32 * q^62 + 70 * q^63 - 8 * q^64 - 56 * q^65 + 4 * q^66 + 98 * q^67 + 6 * q^68 - 16 * q^69 + 210 * q^70 + 16 * q^71 - 16 * q^72 + 146 * q^73 + 30 * q^74 - 18 * q^75 + 88 * q^76 + 190 * q^77 - 36 * q^78 + 76 * q^79 + 52 * q^81 + 8 * q^82 + 150 * q^83 + 38 * q^84 + 16 * q^85 - 14 * q^86 + 224 * q^87 - 4 * q^88 - 24 * q^89 + 292 * q^90 + 26 * q^91 + 6 * q^92 + 46 * q^93 - 8 * q^94 - 80 * q^95 - 2 * q^96 + 32 * q^97 + 12 * q^98 - 50 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(158, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
158.2.e.a	$158$	$2$	158.e	79.e	$13$	$48$	$4$	$1.262$		None		✓			158.2.e.a	$2$	$0$	\(-4\)	\(-2\)	\(11\)	\(-8\)		$\mathrm{SU}(2)[C_{13}]$
158.2.e.b	$158$	$2$	158.e	79.e	$13$	$48$	$4$	$1.262$		None		✓			158.2.e.b	$2$	$0$	\(4\)	\(0\)	\(-11\)	\(-4\)		$\mathrm{SU}(2)[C_{13}]$

Decomposition of \(S_{2}^{\mathrm{old}}(158, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(158, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)