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

• Label: 546.4.g
• Level: $546$
• Weight: $4$
• Character orbit: 546.g
• Rep. character: $\chi_{546}(209,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $448$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(448\)
Trace bound:			\(14\)

Dimensions

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

	Total	New	Old
Modular forms	344	96	248
Cusp forms	328	96	232
Eisenstein series	16	0	16

Trace form

96 * q - 384 * q^4 + 12 * q^7 + 56 * q^9 - 336 * q^15 + 1536 * q^16 + 296 * q^21 + 480 * q^22 + 2160 * q^25 - 48 * q^28 - 728 * q^30 - 224 * q^36 + 120 * q^37 - 476 * q^42 + 2688 * q^43 - 2448 * q^46 - 2268 * q^49 - 1468 * q^51 - 4640 * q^57 + 3024 * q^58 + 1344 * q^60 + 2596 * q^63 - 6144 * q^64 + 192 * q^70 + 1848 * q^79 - 536 * q^81 - 1184 * q^84 + 7392 * q^85 - 1920 * q^88 - 624 * q^91 + 5168 * q^93 - 8904 * q^99

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.g.a	$546$	$4$	546.g	21.c	$2$	$48$	$48$	$32.215$		None		✓			546.4.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{2}]$
546.4.g.b	$546$	$4$	546.g	21.c	$2$	$48$	$48$	$32.215$		None		✓			546.4.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)