Space of modular forms of level 911, weight 2, and trivial character

• Label: 911.2.a
• Level: $911$
• Weight: $2$
• Character orbit: 911.a
• Rep. character: $\chi_{911}(1,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $3$
• Sturm bound: $152$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 911 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	911.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(152\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(911))\).

	Total	New	Old
Modular forms	77	77	0
Cusp forms	76	76	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.

\(911\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(23\)	\(23\)	\(0\)		\(23\)	\(23\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(54\)	\(54\)	\(0\)		\(53\)	\(53\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

76 * q - q^2 + 77 * q^4 + 2 * q^5 + 6 * q^6 + 4 * q^7 + 3 * q^8 + 78 * q^9 + 12 * q^10 - 2 * q^11 - 2 * q^12 + 8 * q^13 - 6 * q^14 - 16 * q^15 + 75 * q^16 + 4 * q^17 - 9 * q^18 + 12 * q^19 + 2 * q^20 - 4 * q^21 - 14 * q^22 - 8 * q^23 + 18 * q^24 + 78 * q^25 + 6 * q^26 + 6 * q^27 + 4 * q^29 + 6 * q^30 + 20 * q^31 + 5 * q^32 - 6 * q^33 - 10 * q^34 - 6 * q^35 + 87 * q^36 - 4 * q^37 - 18 * q^38 + 10 * q^39 + 26 * q^40 + 22 * q^41 - 12 * q^42 + 12 * q^43 - 34 * q^44 - 6 * q^45 + 22 * q^46 + 4 * q^47 - 32 * q^48 + 116 * q^49 - 21 * q^50 - 8 * q^51 + 28 * q^52 - 4 * q^53 + 26 * q^54 + 20 * q^55 - 34 * q^56 + 14 * q^57 + 6 * q^58 - 8 * q^60 + 54 * q^61 + 8 * q^62 - 6 * q^63 + 87 * q^64 + 8 * q^65 + 34 * q^66 - 8 * q^67 - 44 * q^68 + 12 * q^69 - 10 * q^70 - 14 * q^71 - 27 * q^72 + 52 * q^73 - 6 * q^74 - 2 * q^75 + 18 * q^76 + 20 * q^77 - 74 * q^78 + 12 * q^79 - 18 * q^80 + 108 * q^81 + 52 * q^82 - 26 * q^83 - 120 * q^84 + 36 * q^85 - 28 * q^86 + 26 * q^87 - 50 * q^88 + 42 * q^89 + 24 * q^90 - 78 * q^92 + 28 * q^94 - 4 * q^95 + 40 * q^96 + 64 * q^97 - 29 * q^98 - 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(911))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		911
911.2.a.a	$911$	$2$	911.a	1.a	$1$	$9$	$9$	$7.274$	9.9.\(\cdots\).1	None	✓	✓			911.2.a.a	$1$	$1$	\(-5\)	\(1\)	\(-1\)	\(5\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{7})q^{2}-\beta _{5}q^{3}+(\beta _{3}+\beta _{7}+\cdots)q^{4}+\cdots\)
911.2.a.b	$911$	$2$	911.a	1.a	$1$	$14$	$14$	$7.274$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		911.2.a.b	$1$	$1$	\(2\)	\(-7\)	\(-7\)	\(-15\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
911.2.a.c	$911$	$2$	911.a	1.a	$1$	$53$	$53$	$7.274$		None	✓	✓	✓	✓	911.2.a.c	$1$	$0$	\(2\)	\(6\)	\(10\)	\(14\)		$-$	$-$		$\mathrm{SU}(2)$