Space of modular forms of level 121, weight 3, and Character 121.f

• Label: 121.3.f
• Level: $121$
• Weight: $3$
• Character orbit: 121.f
• Rep. character: $\chi_{121}(10,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $210$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	121.f (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(121, [\chi])\).

	Total	New	Old
Modular forms	230	230	0
Cusp forms	210	210	0
Eisenstein series	20	20	0

Trace form

\( 210 q - 11 q^{2} - 16 q^{3} + 25 q^{4} - 7 q^{5} - 55 q^{6} - 11 q^{7} - 11 q^{8} + 534 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
121.3.f.a	$121$	$3$	121.f	121.f	$22$	$210$	$21$	$3.297$		None		$2$	$0$	\(-11\)	\(-16\)	\(-7\)	\(-11\)		$\mathrm{SU}(2)[C_{22}]$