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

• Label: 546.2.p
• Level: $546$
• Weight: $2$
• Character orbit: 546.p
• Rep. character: $\chi_{546}(239,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $4$
• 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.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)
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	56	184
Cusp forms	208	56	152
Eisenstein series	32	0	32

Trace form

\( 56 q + O(q^{10}) \)

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.p.a	$546$	$2$	546.p	39.f	$4$	$8$	$4$	$4.360$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}+(\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
546.2.p.b	$546$	$2$	546.p	39.f	$4$	$8$	$4$	$4.360$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
546.2.p.c	$546$	$2$	546.p	39.f	$4$	$20$	$10$	$4.360$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{8}q^{2}+\beta _{11}q^{3}-\beta _{4}q^{4}+(\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots\)
546.2.p.d	$546$	$2$	546.p	39.f	$4$	$20$	$10$	$4.360$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{2}-\beta _{19}q^{3}-\beta _{4}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)

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

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