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

• Label: 546.2.by
• Level: $546$
• Weight: $2$
• Character orbit: 546.by
• Rep. character: $\chi_{546}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	480	72	408
Cusp forms	416	72	344
Eisenstein series	64	0	64

Trace form

\( 72 q + 4 q^{7} - 72 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
546.2.by.a	$546$	$2$	546.by	91.w	$12$	$32$	$8$	$4.360$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{12}]$
546.2.by.b	$546$	$2$	546.by	91.w	$12$	$40$	$10$	$4.360$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)