Space of modular forms of level 953, weight 2, and trivial character

• Label: 953.2.a
• Level: $953$
• Weight: $2$
• Character orbit: 953.a
• Rep. character: $\chi_{953}(1,\cdot)$
• Character field: $\Q$
• Dimension: $79$
• Newform subspaces: $2$
• Sturm bound: $159$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 953 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	953.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(159\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(953))\).

	Total	New	Old
Modular forms	80	80	0
Cusp forms	79	79	0
Eisenstein series	1	1	0

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

\(953\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(32\)	\(32\)	\(0\)		\(32\)	\(32\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(48\)	\(48\)	\(0\)		\(47\)	\(47\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(953))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		953
953.2.a.a	$953$	$2$	953.a	1.a	$1$	$32$	$32$	$7.610$		None	✓	✓	✓	✓	953.2.a.a	$1$	$1$	\(-5\)	\(-16\)	\(-6\)	\(-38\)		$+$	$+$		$\mathrm{SU}(2)$
953.2.a.b	$953$	$2$	953.a	1.a	$1$	$47$	$47$	$7.610$		None	✓	✓	✓	✓	953.2.a.b	$1$	$0$	\(2\)	\(16\)	\(6\)	\(42\)		$-$	$-$		$\mathrm{SU}(2)$