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

• Label: 546.4.i
• Level: $546$
• Weight: $4$
• Character orbit: 546.i
• Rep. character: $\chi_{546}(79,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $9$
• 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.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
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	96	592
Cusp forms	656	96	560
Eisenstein series	32	0	32

Trace form

96 * q - 192 * q^4 - 32 * q^5 - 48 * q^6 - 4 * q^7 - 432 * q^9 + 24 * q^10 + 112 * q^11 - 104 * q^13 + 40 * q^14 - 168 * q^15 - 768 * q^16 - 516 * q^17 + 152 * q^19 + 256 * q^20 - 736 * q^22 + 120 * q^23 + 96 * q^24 - 636 * q^25 + 176 * q^28 + 552 * q^29 - 48 * q^30 - 76 * q^31 + 276 * q^33 - 608 * q^34 + 432 * q^35 + 3456 * q^36 - 384 * q^37 - 104 * q^38 + 96 * q^40 + 512 * q^41 - 504 * q^42 + 1504 * q^43 + 448 * q^44 - 288 * q^45 - 432 * q^46 + 240 * q^47 - 792 * q^49 - 448 * q^50 - 336 * q^51 + 208 * q^52 - 1188 * q^53 + 216 * q^54 + 1528 * q^55 + 160 * q^56 + 1392 * q^57 + 168 * q^58 + 1968 * q^59 + 336 * q^60 + 1404 * q^61 + 2144 * q^62 - 360 * q^63 + 6144 * q^64 - 832 * q^65 + 224 * q^67 - 2064 * q^68 - 1392 * q^69 - 1976 * q^70 - 5280 * q^71 + 568 * q^73 - 192 * q^74 - 1216 * q^76 - 5296 * q^77 - 1740 * q^79 - 512 * q^80 - 3888 * q^81 - 2560 * q^82 + 7248 * q^83 - 3600 * q^85 + 352 * q^86 + 948 * q^87 + 1472 * q^88 + 2800 * q^89 - 432 * q^90 + 1248 * q^91 - 960 * q^92 + 456 * q^93 + 920 * q^94 + 1128 * q^95 + 384 * q^96 - 4136 * q^97 - 1056 * q^98 - 2016 * 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.i.a	$546$	$4$	546.i	7.c	$3$	$4$	$2$	$32.215$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None		✓			546.4.i.a	$2$	$0$	\(-4\)	\(6\)	\(6\)	\(-20\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{1}q^{2}+(3-3\beta _{1})q^{3}+(-4+4\beta _{1}+\cdots)q^{4}+\cdots\)
546.4.i.b	$546$	$4$	546.i	7.c	$3$	$8$	$4$	$32.215$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			546.4.i.b	$2$	$0$	\(-8\)	\(12\)	\(-34\)	\(35\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{3})q^{2}-3\beta _{3}q^{3}+4\beta _{3}q^{4}+\cdots\)
546.4.i.c	$546$	$4$	546.i	7.c	$3$	$10$	$5$	$32.215$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			546.4.i.c	$2$	$0$	\(-10\)	\(-15\)	\(7\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{6}q^{2}+(-3+3\beta _{6})q^{3}+(-4+4\beta _{6}+\cdots)q^{4}+\cdots\)
546.4.i.d	$546$	$4$	546.i	7.c	$3$	$10$	$5$	$32.215$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			546.4.i.d	$2$	$0$	\(10\)	\(15\)	\(-13\)	\(8\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\beta _{3})q^{2}+3\beta _{3}q^{3}-4\beta _{3}q^{4}+\cdots\)
546.4.i.e	$546$	$4$	546.i	7.c	$3$	$12$	$6$	$32.215$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			546.4.i.e	$2$	$0$	\(-12\)	\(-18\)	\(-7\)	\(-11\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\beta _{1})q^{2}-3\beta _{1}q^{3}-4\beta _{1}q^{4}+\cdots\)
546.4.i.f	$546$	$4$	546.i	7.c	$3$	$12$	$6$	$32.215$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			546.4.i.f	$2$	$0$	\(12\)	\(-18\)	\(-14\)	\(29\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{2}+(-3+3\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
546.4.i.g	$546$	$4$	546.i	7.c	$3$	$12$	$6$	$32.215$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			546.4.i.g	$2$	$0$	\(12\)	\(18\)	\(-7\)	\(-35\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{4}q^{2}+(3+3\beta _{4})q^{3}+(-4-4\beta _{4}+\cdots)q^{4}+\cdots\)
546.4.i.h	$546$	$4$	546.i	7.c	$3$	$14$	$7$	$32.215$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			546.4.i.h	$2$	$0$	\(-14\)	\(21\)	\(18\)	\(10\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{3}q^{2}+(3-3\beta _{3})q^{3}+(-4+4\beta _{3}+\cdots)q^{4}+\cdots\)
546.4.i.i	$546$	$4$	546.i	7.c	$3$	$14$	$7$	$32.215$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			546.4.i.i	$2$	$0$	\(14\)	\(-21\)	\(12\)	\(-14\)	$2^{4}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{4})q^{2}+3\beta _{4}q^{3}+4\beta _{4}q^{4}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)