Space of modular forms of level 889, weight 2, and trivial character

• Label: 889.2.a
• Level: $889$
• Weight: $2$
• Character orbit: 889.a
• Rep. character: $\chi_{889}(1,\cdot)$
• Character field: $\Q$
• Dimension: $63$
• Newform subspaces: $4$
• Sturm bound: $170$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(170\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(889))\).

	Total	New	Old
Modular forms	86	63	23
Cusp forms	83	63	20
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.

\(7\)	\(127\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(19\)	\(16\)	\(3\)		\(19\)	\(16\)	\(3\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(23\)	\(15\)	\(8\)		\(22\)	\(15\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(24\)	\(20\)	\(4\)		\(23\)	\(20\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(20\)	\(12\)	\(8\)		\(19\)	\(12\)	\(7\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(39\)	\(28\)	\(11\)		\(38\)	\(28\)	\(10\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(47\)	\(35\)	\(12\)		\(45\)	\(35\)	\(10\)		\(2\)	\(0\)	\(2\)

Trace form

63 * q - q^2 - 4 * q^3 + 59 * q^4 - 6 * q^5 + q^7 + 3 * q^8 + 51 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^13 + 3 * q^14 - 8 * q^15 + 63 * q^16 - 10 * q^17 - 9 * q^18 - 8 * q^19 - 42 * q^20 - 4 * q^21 - 8 * q^22 + 12 * q^23 - 4 * q^24 + 45 * q^25 + 2 * q^26 - 16 * q^27 + 7 * q^28 - 2 * q^29 + 28 * q^30 - 20 * q^31 + 5 * q^32 - 8 * q^33 - 44 * q^34 - 2 * q^35 + 47 * q^36 - 18 * q^37 + 2 * q^38 + 8 * q^39 - 14 * q^40 - 22 * q^41 + 8 * q^42 + 20 * q^43 + 26 * q^44 - 38 * q^45 - 8 * q^46 - 12 * q^47 - 24 * q^48 + 63 * q^49 - 7 * q^50 - 32 * q^51 + 44 * q^52 - 26 * q^53 - 4 * q^54 + 32 * q^55 + 15 * q^56 - 8 * q^57 + 38 * q^58 + 16 * q^59 - 32 * q^60 - 14 * q^61 + 34 * q^62 + 5 * q^63 + 47 * q^64 + 44 * q^66 + 28 * q^67 - 66 * q^68 - 16 * q^69 - 18 * q^70 - 20 * q^71 + 27 * q^72 - 46 * q^73 - 20 * q^74 - 76 * q^75 - 60 * q^76 + 12 * q^77 - 48 * q^78 - 16 * q^79 - 26 * q^80 + 31 * q^81 + 14 * q^82 - 44 * q^83 - 56 * q^85 - 4 * q^86 + 20 * q^87 - 6 * q^88 - 6 * q^89 + 38 * q^90 - 6 * q^91 + 84 * q^92 + 4 * q^93 + 40 * q^94 + 44 * q^95 - 20 * q^96 - 34 * q^97 - q^98 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(889))\) 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	127
889.2.a.a	$889$	$2$	889.a	1.a	$1$	$12$	$12$	$7.099$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓	✓	889.2.a.a	$1$	$1$	\(-7\)	\(-4\)	\(-7\)	\(12\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{10}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
889.2.a.b	$889$	$2$	889.a	1.a	$1$	$15$	$15$	$7.099$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	889.2.a.b	$1$	$0$	\(0\)	\(4\)	\(7\)	\(-15\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
889.2.a.c	$889$	$2$	889.a	1.a	$1$	$16$	$16$	$7.099$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	889.2.a.c	$1$	$1$	\(-2\)	\(-4\)	\(-9\)	\(-16\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
889.2.a.d	$889$	$2$	889.a	1.a	$1$	$20$	$20$	$7.099$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	889.2.a.d	$1$	$0$	\(8\)	\(0\)	\(3\)	\(20\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{16}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(889))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(889)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(127))\)\(^{\oplus 2}\)