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

• Label: 546.2.e
• Level: $546$
• Weight: $2$
• Character orbit: 546.e
• Rep. character: $\chi_{546}(545,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $8$
• Sturm bound: $224$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(224\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\), \(17\), \(19\), \(71\)

Dimensions

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

	Total	New	Old
Modular forms	120	40	80
Cusp forms	104	40	64
Eisenstein series	16	0	16

Trace form

\( 40 q + 40 q^{4} - 8 q^{9} + O(q^{10}) \)

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.e.a	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(-3\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
546.2.e.b	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(3\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
546.2.e.c	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-3\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
546.2.e.d	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(3\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
546.2.e.e	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	8.0.303595776.1	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{5}+\beta _{7})q^{5}+\cdots\)
546.2.e.f	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	8.0.\(\cdots\).11	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)
546.2.e.g	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	8.0.303595776.1	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{5}-\beta _{7})q^{5}+\cdots\)
546.2.e.h	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	8.0.\(\cdots\).11	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)

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

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