Space of modular forms of level 546, weight 2, and Character 546.bg

• Label: 546.2.bg
• Level: $546$
• Weight: $2$
• Character orbit: 546.bg
• Rep. character: $\chi_{546}(311,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(546, [\chi])\).

	Total	New	Old
Modular forms	240	72	168
Cusp forms	208	72	136
Eisenstein series	32	0	32

Trace form

72 * q - 36 * q^4 + 8 * q^9 - 36 * q^16 + 28 * q^25 + 14 * q^30 - 16 * q^36 - 32 * q^42 - 32 * q^43 + 24 * q^49 - 6 * q^51 + 12 * q^52 - 72 * q^61 + 72 * q^64 - 48 * q^66 + 108 * q^75 + 40 * q^78 + 40 * q^79 - 40 * q^81 - 48 * q^82 - 48 * q^87 - 4 * q^91 - 144 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(546, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
546.2.bg.a	$546$	$2$	546.bg	273.aa	$6$	$36$	$18$	$4.360$		None		✓			546.2.bg.a	$4$	$0$	\(-18\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
546.2.bg.b	$546$	$2$	546.bg	273.aa	$6$	$36$	$18$	$4.360$		None		✓			546.2.bg.a	$4$	$0$	\(18\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)