Space of modular forms of level 950, weight 2, and Character 950.bg

• Label: 950.2.bg
• Level: $950$
• Weight: $2$
• Character orbit: 950.bg
• Rep. character: $\chi_{950}(9,\cdot)$
• Character field: $\Q(\zeta_{90})$
• Dimension: $1200$
• Newform subspaces: $1$
• Sturm bound: $300$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bg (of order \(90\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 475 \)
Character field:			\(\Q(\zeta_{90})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(300\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(950, [\chi])\).

	Total	New	Old
Modular forms	3696	1200	2496
Cusp forms	3504	1200	2304
Eisenstein series	192	0	192

Trace form

\( 1200 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
950.2.bg.a	$950$	$2$	950.bg	475.ag	$90$	$1200$	$50$	$7.586$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{90}]$

Decomposition of \(S_{2}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)