Space of modular forms of level 650, weight 2, and Character 650.ba

• Label: 650.2.ba
• Level: $650$
• Weight: $2$
• Character orbit: 650.ba
• Rep. character: $\chi_{650}(73,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $280$
• Newform subspaces: $2$
• Sturm bound: $210$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.ba (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(210\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

	Total	New	Old
Modular forms	872	280	592
Cusp forms	808	280	528
Eisenstein series	64	0	64

Trace form

\( 280 q + 2 q^{2} - 70 q^{4} + 2 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
650.2.ba.a	$650$	$2$	650.ba	325.z	$20$	$136$	$17$	$5.190$		None		$2$	$0$	\(-34\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
650.2.ba.b	$650$	$2$	650.ba	325.z	$20$	$144$	$18$	$5.190$		None		$2$	$0$	\(36\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)