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

• Label: 650.2.bg
• Level: $650$
• Weight: $2$
• Character orbit: 650.bg
• Rep. character: $\chi_{650}(9,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $272$
• Newform subspaces: $1$
• Sturm bound: $210$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.bg (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(210\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	880	272	608
Cusp forms	816	272	544
Eisenstein series	64	0	64

Trace form

272 * q - 34 * q^4 - 30 * q^9 + 2 * q^10 - 16 * q^14 + 36 * q^15 + 34 * q^16 - 24 * q^19 - 20 * q^23 + 36 * q^25 + 4 * q^26 + 4 * q^29 + 16 * q^30 + 120 * q^33 + 6 * q^35 + 30 * q^36 - 10 * q^37 - 52 * q^39 + 4 * q^40 - 22 * q^41 + 48 * q^45 + 100 * q^47 + 104 * q^49 + 8 * q^50 - 80 * q^51 - 80 * q^53 - 12 * q^54 - 42 * q^55 - 8 * q^56 - 12 * q^59 - 8 * q^60 - 12 * q^61 - 60 * q^62 + 70 * q^63 + 68 * q^64 - 40 * q^65 + 32 * q^66 + 50 * q^69 - 104 * q^70 - 32 * q^71 - 160 * q^73 - 84 * q^74 - 142 * q^75 - 16 * q^76 + 240 * q^77 - 110 * q^78 - 16 * q^79 - 26 * q^81 - 140 * q^83 + 36 * q^85 - 24 * q^86 - 80 * q^87 + 42 * q^89 + 40 * q^90 - 100 * q^91 + 40 * q^92 + 8 * q^95 - 40 * q^98 + 40 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
650.2.bg.a	$650$	$2$	650.bg	325.af	$30$	$272$	$34$	$5.190$		None		✓	✓	✓	650.2.bg.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$

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

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