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

• Label: 546.4.c
• Level: $546$
• Weight: $4$
• Character orbit: 546.c
• Rep. character: $\chi_{546}(337,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
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	344	44	300
Cusp forms	328	44	284
Eisenstein series	16	0	16

Trace form

44 * q - 176 * q^4 + 396 * q^9 - 128 * q^10 - 168 * q^13 + 704 * q^16 + 368 * q^17 + 176 * q^22 - 544 * q^23 - 900 * q^25 + 288 * q^26 - 576 * q^29 - 240 * q^30 + 112 * q^35 - 1584 * q^36 - 416 * q^38 + 24 * q^39 + 512 * q^40 + 168 * q^42 - 1584 * q^43 - 2156 * q^49 - 528 * q^51 + 672 * q^52 - 3088 * q^53 - 960 * q^55 - 3168 * q^61 - 2816 * q^64 + 768 * q^65 + 1248 * q^66 - 1472 * q^68 - 2496 * q^69 - 2336 * q^74 - 896 * q^77 + 264 * q^78 + 3416 * q^79 + 3564 * q^81 + 1808 * q^82 - 1320 * q^87 - 704 * q^88 - 1152 * q^90 + 420 * q^91 + 2176 * q^92 - 2832 * q^94 + 1800 * q^95

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

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

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