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

• Label: 546.2.bq
• Level: $546$
• Weight: $2$
• Character orbit: 546.bq
• Rep. character: $\chi_{546}(419,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $224$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(224\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(5\), \(61\)

Dimensions

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

	Total	New	Old
Modular forms	240	72	168
Cusp forms	208	72	136
Eisenstein series	32	0	32

Trace form

72 * q + 36 * q^4 + 8 * q^7 + 4 * q^9 + 12 * q^15 - 36 * q^16 - 24 * q^18 + 16 * q^21 + 56 * q^25 - 8 * q^28 + 8 * q^30 - 4 * q^36 - 16 * q^37 - 48 * q^39 + 8 * q^42 - 12 * q^43 - 4 * q^46 + 4 * q^49 + 16 * q^51 + 8 * q^57 - 8 * q^58 + 24 * q^60 + 8 * q^63 - 72 * q^64 + 52 * q^67 - 12 * q^72 + 36 * q^78 + 16 * q^79 + 32 * q^81 + 8 * q^84 - 88 * q^85 - 64 * q^91 - 56 * q^93

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
546.2.bq.a	$546$	$2$	546.bq	273.an	$6$	$4$	$2$	$4.360$	\(\Q(\zeta_{12})\)	None		✓			546.2.bq.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.bq.b	$546$	$2$	546.bq	273.an	$6$	$4$	$2$	$4.360$	\(\Q(\zeta_{12})\)	None		✓			546.2.bq.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.bq.c	$546$	$2$	546.bq	273.an	$6$	$64$	$32$	$4.360$		None		✓	✓		546.2.bq.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$\mathrm{SU}(2)[C_{6}]$

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

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