Space of modular forms of level 11, weight 2, and trivial character

• Label: 11.2.a
• Level: $11$
• Weight: $2$
• Character orbit: 11.a
• Rep. character: $\chi_{11}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(11))\).

	Total	New	Old
Modular forms	2	2	0
Cusp forms	1	1	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.

\(11\)	Dim
\(-\)	\(1\)

Trace form

q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^9 - 2 * q^10 + q^11 - 2 * q^12 + 4 * q^13 + 4 * q^14 - q^15 - 4 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^20 + 2 * q^21 - 2 * q^22 - q^23 - 4 * q^25 - 8 * q^26 + 5 * q^27 - 4 * q^28 + 2 * q^30 + 7 * q^31 + 8 * q^32 - q^33 + 4 * q^34 - 2 * q^35 - 4 * q^36 + 3 * q^37 - 4 * q^39 - 8 * q^41 - 4 * q^42 - 6 * q^43 + 2 * q^44 - 2 * q^45 + 2 * q^46 + 8 * q^47 + 4 * q^48 - 3 * q^49 + 8 * q^50 + 2 * q^51 + 8 * q^52 - 6 * q^53 - 10 * q^54 + q^55 + 5 * q^59 - 2 * q^60 + 12 * q^61 - 14 * q^62 + 4 * q^63 - 8 * q^64 + 4 * q^65 + 2 * q^66 - 7 * q^67 - 4 * q^68 + q^69 + 4 * q^70 - 3 * q^71 + 4 * q^73 - 6 * q^74 + 4 * q^75 - 2 * q^77 + 8 * q^78 - 10 * q^79 - 4 * q^80 + q^81 + 16 * q^82 - 6 * q^83 + 4 * q^84 - 2 * q^85 + 12 * q^86 + 15 * q^89 + 4 * q^90 - 8 * q^91 - 2 * q^92 - 7 * q^93 - 16 * q^94 - 8 * q^96 - 7 * q^97 + 6 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\) 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
11.2.a.a	$11$	$2$	11.a	1.a	$1$	$1$	$1$	$0.088$	\(\Q\)	None	✓	✓	✓	✓	11.2.a.a	$1$	$0$	\(-2\)	\(-1\)	\(1\)	\(-2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)