Space of modular forms of level 975, weight 2, and Character 975.bx

• Label: 975.2.bx
• Level: $975$
• Weight: $2$
• Character orbit: 975.bx
• Rep. character: $\chi_{975}(73,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $560$
• Newform subspaces: $1$
• Sturm bound: $280$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bx (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(280\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(975, [\chi])\).

	Total	New	Old
Modular forms	1152	560	592
Cusp forms	1088	560	528
Eisenstein series	64	0	64

Trace form

\( 560 q + 4 q^{2} - 140 q^{4} + 4 q^{5} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(975, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
975.2.bx.a	$975$	$2$	975.bx	325.z	$20$	$560$	$70$	$7.785$		None		$2$	$0$	\(4\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(975, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(975, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)