Space of modular forms of level 105, weight 2, and Character 105.x

• Label: 105.2.x
• Level: $105$
• Weight: $2$
• Character orbit: 105.x
• Rep. character: $\chi_{105}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

	Total	New	Old
Modular forms	80	80	0
Cusp forms	48	48	0
Eisenstein series	32	32	0

Trace form

\( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.2.x.a	$105$	$2$	105.x	105.x	$12$	$48$	$12$	$0.838$		None		✓	✓	✓	105.2.x.a	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$