Space of modular forms of level 546, weight 4, and Character 546.s

• Label: 546.4.s
• Level: $546$
• Weight: $4$
• Character orbit: 546.s
• Rep. character: $\chi_{546}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $4$
• Sturm bound: $448$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(448\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(546, [\chi])\).

	Total	New	Old
Modular forms	688	88	600
Cusp forms	656	88	568
Eisenstein series	32	0	32

Trace form

88 * q + 176 * q^4 - 396 * q^9 - 64 * q^10 - 240 * q^11 - 120 * q^13 - 144 * q^15 - 704 * q^16 + 184 * q^17 + 288 * q^20 - 176 * q^22 - 536 * q^23 - 2616 * q^25 - 288 * q^26 - 240 * q^29 + 240 * q^30 - 1152 * q^33 - 112 * q^35 + 1584 * q^36 + 840 * q^37 + 416 * q^38 - 24 * q^39 - 512 * q^40 - 336 * q^41 - 168 * q^42 + 180 * q^43 - 648 * q^45 + 792 * q^46 + 2156 * q^49 + 1152 * q^50 - 696 * q^51 - 192 * q^52 - 848 * q^53 + 2256 * q^55 - 3024 * q^58 - 2328 * q^59 - 1584 * q^61 - 5632 * q^64 - 1128 * q^65 - 1248 * q^66 - 2316 * q^67 - 736 * q^68 - 1248 * q^69 - 4056 * q^71 - 1168 * q^74 + 896 * q^77 + 528 * q^78 - 1712 * q^79 + 1152 * q^80 - 3564 * q^81 + 112 * q^82 - 2856 * q^85 - 48 * q^87 + 704 * q^88 + 504 * q^89 + 1152 * q^90 + 840 * q^91 - 4288 * q^92 - 1056 * q^94 - 3048 * q^95 + 840 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(546, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
546.4.s.a	$546$	$4$	546.s	13.e	$6$	$20$	$10$	$32.215$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			546.4.s.a	$2$	$0$	\(0\)	\(-30\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{4}q^{2}+(-3+3\beta _{6})q^{3}+4\beta _{6}q^{4}+\cdots\)
546.4.s.b	$546$	$4$	546.s	13.e	$6$	$20$	$10$	$32.215$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			546.4.s.b	$2$	$0$	\(0\)	\(30\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{4}q^{2}+3\beta _{7}q^{3}+(4-4\beta _{7})q^{4}+\cdots\)
546.4.s.c	$546$	$4$	546.s	13.e	$6$	$24$	$12$	$32.215$		None		✓			546.4.s.c	$2$	$0$	\(0\)	\(-36\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
546.4.s.d	$546$	$4$	546.s	13.e	$6$	$24$	$12$	$32.215$		None		✓			546.4.s.d	$2$	$0$	\(0\)	\(36\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)