Space of modular forms of level 123, weight 3, and Character 123.h

• Label: 123.3.h
• Level: $123$
• Weight: $3$
• Character orbit: 123.h
• Rep. character: $\chi_{123}(55,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	123.h (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(123, [\chi])\).

	Total	New	Old
Modular forms	120	56	64
Cusp forms	104	56	48
Eisenstein series	16	0	16

Trace form

\( 56 q + 8 q^{2} - 48 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(123, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
123.3.h.a	$123$	$3$	123.h	41.e	$8$	$56$	$14$	$3.352$		None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(123, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(123, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)