Space of modular forms of level 123, weight 2, and Character 123.n

• Label: 123.2.n
• Level: $123$
• Weight: $2$
• Character orbit: 123.n
• Rep. character: $\chi_{123}(43,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	123.n (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(123, [\chi])\).

	Total	New	Old
Modular forms	128	48	80
Cusp forms	96	48	48
Eisenstein series	32	0	32

Trace form

\( 48 q + 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(123, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
123.2.n.a	$123$	$2$	123.n	41.g	$20$	$48$	$6$	$0.982$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(123, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(123, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)