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

• Label: 546.2.c
• Level: $546$
• Weight: $2$
• Character orbit: 546.c
• Rep. character: $\chi_{546}(337,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	120	12	108
Cusp forms	104	12	92
Eisenstein series	16	0	16

Trace form

\( 12 q - 12 q^{4} + 12 q^{9} + O(q^{10}) \)

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.c.a	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}-iq^{5}-iq^{6}+iq^{7}+\cdots\)
546.2.c.b	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
546.2.c.c	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}-iq^{7}+\cdots\)
546.2.c.d	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots\)
546.2.c.e	$546$	$2$	546.c	13.b	$2$	$4$	$4$	$4.360$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)