Space of modular forms of level 143, weight 2, and Character 143.e

• Label: 143.2.e
• Level: $143$
• Weight: $2$
• Character orbit: 143.e
• Rep. character: $\chi_{143}(100,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $28$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(143, [\chi])\).

	Total	New	Old
Modular forms	32	24	8
Cusp forms	24	24	0
Eisenstein series	8	0	8

Trace form

24 * q - 2 * q^2 - 2 * q^3 - 12 * q^4 - 8 * q^5 + 6 * q^6 - 2 * q^7 - 14 * q^9 + 6 * q^10 - 4 * q^12 - 10 * q^13 + 8 * q^14 - 16 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 2 * q^19 + 14 * q^20 - 20 * q^21 - 2 * q^22 - 6 * q^23 + 12 * q^24 + 8 * q^25 + 2 * q^26 + 16 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 + 4 * q^31 - 22 * q^32 - 4 * q^34 - 16 * q^35 - 20 * q^36 + 10 * q^37 + 20 * q^38 + 16 * q^39 - 76 * q^40 + 20 * q^41 + 2 * q^42 + 18 * q^43 - 8 * q^44 + 14 * q^45 + 38 * q^46 - 48 * q^47 + 8 * q^48 - 2 * q^49 - 26 * q^50 - 28 * q^51 + 22 * q^52 + 8 * q^53 + 32 * q^54 - 8 * q^55 - 6 * q^56 + 16 * q^57 - 24 * q^58 - 16 * q^59 + 100 * q^60 + 30 * q^61 + 12 * q^62 - 6 * q^63 - 28 * q^64 - 24 * q^65 + 36 * q^66 - 6 * q^67 + 12 * q^68 + 18 * q^69 - 84 * q^70 - 10 * q^71 - 68 * q^72 - 20 * q^73 + 58 * q^74 + 6 * q^75 - 16 * q^76 + 16 * q^77 + 60 * q^78 - 8 * q^79 + 48 * q^80 - 4 * q^81 - 14 * q^82 - 44 * q^83 + 16 * q^84 - 36 * q^85 - 76 * q^86 + 8 * q^87 + 6 * q^88 - 10 * q^89 - 64 * q^90 + 46 * q^91 + 44 * q^92 - 70 * q^93 + 6 * q^94 + 4 * q^95 + 80 * q^96 - 14 * q^97 + 56 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(143, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
143.2.e.a	$143$	$2$	143.e	13.c	$3$	$6$	$3$	$1.142$	6.0.1714608.1	None		✓			143.2.e.a	$2$	$0$	\(-3\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{4})q^{2}+(-\beta _{3}+\beta _{5})q^{3}-\beta _{4}q^{4}+\cdots\)
143.2.e.b	$143$	$2$	143.e	13.c	$3$	$6$	$3$	$1.142$	6.0.3518667.1	None		✓			143.2.e.b	$2$	$0$	\(1\)	\(-1\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-3+\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
143.2.e.c	$143$	$2$	143.e	13.c	$3$	$12$	$6$	$1.142$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		143.2.e.c	$2$	$0$	\(0\)	\(-1\)	\(-12\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{6}q^{2}+(\beta _{6}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)