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

• Label: 546.2.g
• Level: $546$
• Weight: $2$
• Character orbit: 546.g
• Rep. character: $\chi_{546}(209,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	120	32	88
Cusp forms	104	32	72
Eisenstein series	16	0	16

Trace form

\( 32 q - 32 q^{4} - 4 q^{7} + 8 q^{9} + O(q^{10}) \)

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.g.a	$546$	$2$	546.g	21.c	$2$	$4$	$4$	$4.360$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.g.b	$546$	$2$	546.g	21.c	$2$	$4$	$4$	$4.360$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
546.2.g.c	$546$	$2$	546.g	21.c	$2$	$12$	$12$	$4.360$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{4}q^{5}+\beta _{6}q^{6}+\cdots\)
546.2.g.d	$546$	$2$	546.g	21.c	$2$	$12$	$12$	$4.360$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{6}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)