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

• Label: 546.2.bn
• Level: $546$
• Weight: $2$
• Character orbit: 546.bn
• Rep. character: $\chi_{546}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $6$
• 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.bn (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
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	240	76	164
Cusp forms	208	76	132
Eisenstein series	32	0	32

Trace form

\( 76 q - 38 q^{4} + 2 q^{7} + 8 q^{9} + O(q^{10}) \)

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.bn.a	$546$	$2$	546.bn	273.y	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-3\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.b	$546$	$2$	546.bn	273.y	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-6\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{6}q^{2}+(-1+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.c	$546$	$2$	546.bn	273.y	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(6\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{6}q^{2}+(-1+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.d	$546$	$2$	546.bn	273.y	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.e	$546$	$2$	546.bn	273.y	$6$	$34$	$17$	$4.360$		None		$2$	$0$	\(-17\)	\(3\)	\(9\)	\(5\)		$\mathrm{SU}(2)[C_{6}]$
546.2.bn.f	$546$	$2$	546.bn	273.y	$6$	$34$	$17$	$4.360$		None		$2$	$0$	\(17\)	\(-3\)	\(-9\)	\(5\)		$\mathrm{SU}(2)[C_{6}]$

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

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