Space of modular forms of level 1589, weight 2, and trivial character

• Label: 1589.2.a
• Level: $1589$
• Weight: $2$
• Character orbit: 1589.a
• Rep. character: $\chi_{1589}(1,\cdot)$
• Character field: $\Q$
• Dimension: $113$
• Newform subspaces: $4$
• Sturm bound: $304$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1589 = 7 \cdot 227 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1589.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(304\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1589))\).

	Total	New	Old
Modular forms	154	113	41
Cusp forms	151	113	38
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.

\(7\)	\(227\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(27\)	\(22\)	\(5\)		\(27\)	\(22\)	\(5\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(50\)	\(35\)	\(15\)		\(49\)	\(35\)	\(14\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(40\)	\(34\)	\(6\)		\(39\)	\(34\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(37\)	\(22\)	\(15\)		\(36\)	\(22\)	\(14\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(64\)	\(44\)	\(20\)		\(63\)	\(44\)	\(19\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(90\)	\(69\)	\(21\)		\(88\)	\(69\)	\(19\)		\(2\)	\(0\)	\(2\)

Trace form

113 * q - q^2 + 115 * q^4 - 6 * q^5 - q^7 - 9 * q^8 + 117 * q^9 + 6 * q^10 - 4 * q^11 - 6 * q^13 + q^14 + 4 * q^15 + 123 * q^16 - 2 * q^17 - 21 * q^18 + 20 * q^19 - 42 * q^20 - 4 * q^22 + 8 * q^24 + 95 * q^25 - 2 * q^26 - 12 * q^27 - 7 * q^28 - 6 * q^29 + 4 * q^30 - 9 * q^32 + 20 * q^33 + 18 * q^34 + 6 * q^35 + 151 * q^36 - 22 * q^37 + 8 * q^38 + 34 * q^40 - 2 * q^41 + 12 * q^42 + 32 * q^43 + 24 * q^44 - 58 * q^45 + 24 * q^46 + 16 * q^47 + 20 * q^48 + 113 * q^49 + 45 * q^50 + 48 * q^51 + 2 * q^52 - 26 * q^53 + 36 * q^54 + 28 * q^55 - 3 * q^56 + 16 * q^57 - 10 * q^58 - 10 * q^61 - 20 * q^62 - 5 * q^63 + 123 * q^64 - 4 * q^65 - 32 * q^66 + 8 * q^67 + 22 * q^68 - 44 * q^69 - 18 * q^70 + 4 * q^71 - 93 * q^72 - 6 * q^73 - 2 * q^74 - 44 * q^75 + 80 * q^76 - 4 * q^77 - 72 * q^78 - 40 * q^79 - 94 * q^80 + 113 * q^81 - 58 * q^82 - 12 * q^83 + 16 * q^84 - 48 * q^85 - 16 * q^86 - 4 * q^87 + 16 * q^88 - 42 * q^89 - 46 * q^90 + 14 * q^91 - 36 * q^92 - 104 * q^93 + 60 * q^94 + 28 * q^95 - 32 * q^96 - 6 * q^97 - q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1589))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	227
1589.2.a.a	$1589$	$2$	1589.a	1.a	$1$	$22$	$22$	$12.688$		None	✓	✓	✓	✓	1589.2.a.a	$1$	$1$	\(-3\)	\(-3\)	\(1\)	\(-22\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1589.2.a.b	$1589$	$2$	1589.a	1.a	$1$	$22$	$22$	$12.688$		None	✓	✓	✓	✓	1589.2.a.b	$1$	$1$	\(-1\)	\(-11\)	\(-11\)	\(22\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
1589.2.a.c	$1589$	$2$	1589.a	1.a	$1$	$34$	$34$	$12.688$		None	✓	✓	✓	✓	1589.2.a.c	$1$	$0$	\(1\)	\(11\)	\(11\)	\(34\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1589.2.a.d	$1589$	$2$	1589.a	1.a	$1$	$35$	$35$	$12.688$		None	✓	✓	✓	✓	1589.2.a.d	$1$	$0$	\(2\)	\(3\)	\(-7\)	\(-35\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1589))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1589)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(227))\)\(^{\oplus 2}\)