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

• Label: 546.2.s
• Level: $546$
• Weight: $2$
• Character orbit: 546.s
• Rep. character: $\chi_{546}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(11\)
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	240	24	216
Cusp forms	208	24	184
Eisenstein series	32	0	32

Trace form

24 * q + 12 * q^4 - 12 * q^9 + 24 * q^11 + 8 * q^13 + 24 * q^15 - 12 * q^16 + 8 * q^17 + 8 * q^22 + 8 * q^23 - 40 * q^25 - 8 * q^30 - 24 * q^33 - 8 * q^35 + 12 * q^36 + 16 * q^38 + 8 * q^39 - 24 * q^41 + 4 * q^42 - 12 * q^43 + 12 * q^46 + 12 * q^49 + 8 * q^51 + 16 * q^52 - 64 * q^53 - 8 * q^55 - 24 * q^58 + 96 * q^59 + 8 * q^61 - 24 * q^64 + 24 * q^65 - 16 * q^66 + 36 * q^67 - 8 * q^68 - 8 * q^69 + 24 * q^71 - 8 * q^74 - 32 * q^77 + 8 * q^78 + 32 * q^79 - 12 * q^81 + 8 * q^82 - 72 * q^85 - 16 * q^87 - 8 * q^88 - 72 * q^89 + 8 * q^91 + 16 * q^92 - 16 * q^94 - 48 * q^95

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.s.a	$546$	$2$	546.s	13.e	$6$	$4$	$2$	$4.360$	\(\Q(\zeta_{12})\)	None		✓			546.2.s.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.b	$546$	$2$	546.s	13.e	$6$	$4$	$2$	$4.360$	\(\Q(\zeta_{12})\)	None		✓			546.2.s.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.c	$546$	$2$	546.s	13.e	$6$	$4$	$2$	$4.360$	\(\Q(\zeta_{12})\)	None		✓			546.2.s.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.d	$546$	$2$	546.s	13.e	$6$	$4$	$2$	$4.360$	\(\Q(\zeta_{12})\)	None		✓			546.2.s.d	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.e	$546$	$2$	546.s	13.e	$6$	$8$	$4$	$4.360$	8.0.195105024.2	None		✓	✓		546.2.s.e	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(1+\beta _{4})q^{3}-\beta _{4}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)