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

• Label: 546.2.bx
• Level: $546$
• Weight: $2$
• Character orbit: 546.bx
• Rep. character: $\chi_{546}(97,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bx (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	480	80	400
Cusp forms	416	80	336
Eisenstein series	64	0	64

Trace form

80 * q + 40 * q^9 + 16 * q^11 - 16 * q^14 + 40 * q^16 + 8 * q^21 + 16 * q^22 + 8 * q^35 + 80 * q^37 - 32 * q^39 + 48 * q^43 + 16 * q^44 - 8 * q^46 - 24 * q^49 - 32 * q^50 + 64 * q^53 + 24 * q^56 + 16 * q^57 - 72 * q^58 - 32 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^74 - 16 * q^78 - 96 * q^79 - 40 * q^81 - 16 * q^84 + 16 * q^85 - 16 * q^86 - 16 * q^91 - 32 * q^92 - 48 * q^93 - 192 * q^95 - 16 * q^99

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.bx.a	$546$	$2$	546.bx	91.ac	$12$	$40$	$10$	$4.360$		None		✓			546.2.bx.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$
546.2.bx.b	$546$	$2$	546.bx	91.ac	$12$	$40$	$10$	$4.360$		None		✓			546.2.bx.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{12}]$

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

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