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

• Label: 546.2.i
• Level: $546$
• Weight: $2$
• Character orbit: 546.i
• Rep. character: $\chi_{546}(79,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $11$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	240	32	208
Cusp forms	208	32	176
Eisenstein series	32	0	32

Trace form

\( 32 q - 16 q^{4} + 8 q^{5} + 8 q^{6} - 12 q^{7} - 16 q^{9} + O(q^{10}) \)

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.i.a	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.b	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.c	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.d	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.e	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.f	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.g	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.h	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
546.2.i.i	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-2\)	\(2\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
546.2.i.j	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(2\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.i.k	$546$	$2$	546.i	7.c	$3$	$6$	$3$	$4.360$	6.0.21870000.1	None		$2$	$0$	\(3\)	\(3\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)