Space of modular forms of level 121, weight 2, and trivial character

• Label: 121.2.a
• Level: $121$
• Weight: $2$
• Character orbit: 121.a
• Rep. character: $\chi_{121}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $4$
• Sturm bound: $22$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(22\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(121))\).

	Total	New	Old
Modular forms	17	13	4
Cusp forms	6	4	2
Eisenstein series	11	9	2

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

\(11\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(7\)	\(5\)	\(2\)		\(2\)	\(1\)	\(1\)		\(5\)	\(4\)	\(1\)
\(-\)		\(10\)	\(8\)	\(2\)		\(4\)	\(3\)	\(1\)		\(6\)	\(5\)	\(1\)

Trace form

4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^9 + 2 * q^10 - 4 * q^12 - 4 * q^13 + 6 * q^15 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 6 * q^20 - 2 * q^21 - 6 * q^23 - 8 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 - 2 * q^30 - 2 * q^31 - 8 * q^32 - 6 * q^34 + 2 * q^35 - 2 * q^36 + 4 * q^37 + 12 * q^38 + 4 * q^39 + 8 * q^41 - 12 * q^42 + 6 * q^43 + 6 * q^45 - 2 * q^46 - 4 * q^48 - 16 * q^49 - 8 * q^50 - 2 * q^51 - 8 * q^52 + 18 * q^53 + 10 * q^54 + 12 * q^56 + 18 * q^58 + 6 * q^59 - 12 * q^60 - 12 * q^61 + 14 * q^62 - 4 * q^63 - 2 * q^64 - 4 * q^65 + 10 * q^67 + 4 * q^68 + 18 * q^69 + 18 * q^71 - 4 * q^73 + 6 * q^74 - 16 * q^75 + 12 * q^78 + 10 * q^79 - 18 * q^80 - 20 * q^81 + 6 * q^82 + 6 * q^83 - 4 * q^84 + 2 * q^85 + 12 * q^86 - 12 * q^89 - 4 * q^90 - 12 * q^91 + 12 * q^92 - 10 * q^93 + 16 * q^94 + 8 * q^96 - 16 * q^97 - 6 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(121))\) 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
121.2.a.a	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	\(\Q\)	None	✓	✓			121.2.a.a	$1$	$0$	\(-1\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
121.2.a.b	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	✓	✓	✓	121.2.a.b	$2$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-q^{3}-2q^{4}-3q^{5}-2q^{9}+2q^{12}+\cdots\)
121.2.a.c	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	\(\Q\)	None	✓	✓			121.2.a.a	$1$	$0$	\(1\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}-q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
121.2.a.d	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	\(\Q\)	None	✓				11.2.a.a	$1$	$0$	\(2\)	\(-1\)	\(1\)	\(2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(121))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(121)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)