Space of modular forms of level 143, weight 2, and trivial character

• Label: 143.2.a
• Level: $143$
• Weight: $2$
• Character orbit: 143.a
• Rep. character: $\chi_{143}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $3$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(143))\).

	Total	New	Old
Modular forms	16	11	5
Cusp forms	13	11	2
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(11\)	\(13\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(7\)	\(6\)	\(1\)		\(6\)	\(6\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(6\)	\(4\)	\(2\)		\(5\)	\(4\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(13\)	\(10\)	\(3\)		\(11\)	\(10\)	\(1\)		\(2\)	\(0\)	\(2\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(143))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	13
143.2.a.a	$143$	$2$	143.a	1.a	$1$	$1$	$1$	$1.142$	\(\Q\)	None	✓	✓	✓	✓	143.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\)
143.2.a.b	$143$	$2$	143.a	1.a	$1$	$4$	$4$	$1.142$	4.4.1957.1	None	✓	✓	✓	✓	143.2.a.b	$1$	$0$	\(3\)	\(0\)	\(0\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
143.2.a.c	$143$	$2$	143.a	1.a	$1$	$6$	$6$	$1.142$	6.6.194616205.1	None	✓	✓	✓	✓	143.2.a.c	$1$	$0$	\(0\)	\(3\)	\(1\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(143))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(143)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)