Space of modular forms of level 928, weight 3, and Character 928.b

• Label: 928.3.b
• Level: $928$
• Weight: $3$
• Character orbit: 928.b
• Rep. character: $\chi_{928}(463,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $3$
• Sturm bound: $360$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	928.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 232 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(360\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(3\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(928, [\chi])\).

	Total	New	Old
Modular forms	248	62	186
Cusp forms	232	58	174
Eisenstein series	16	4	12

Trace form

\( 58 q - 166 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(928, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
928.3.b.a	$928$	$3$	928.b	232.b	$2$	$1$	$1$	$25.286$	\(\Q\)	\(\Q(\sqrt{-58}) \)	✓		232.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{9}+5^{2}q^{25}-29q^{29}+54q^{31}+\cdots\)
928.3.b.b	$928$	$3$	928.b	232.b	$2$	$1$	$1$	$25.286$	\(\Q\)	\(\Q(\sqrt{-58}) \)	✓		232.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{9}+5^{2}q^{25}+29q^{29}-54q^{31}+\cdots\)
928.3.b.c	$928$	$3$	928.b	232.b	$2$	$56$	$56$	$25.286$		None			232.3.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(928, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(928, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 2}\)