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

• Label: 123.2.j
• Level: $123$
• Weight: $2$
• Character orbit: 123.j
• Rep. character: $\chi_{123}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	123.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{10})\)
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	64	32	32
Cusp forms	48	32	16
Eisenstein series	16	0	16

Trace form

\( 32 q - 2 q^{2} - 10 q^{4} + 8 q^{5} + 6 q^{8} - 32 q^{9} + O(q^{10}) \)

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.j.a	$123$	$2$	123.j	41.f	$10$	$32$	$8$	$0.982$		None		$2$	$0$	\(-2\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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