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

• Label: 546.2.j
• Level: $546$
• Weight: $2$
• Character orbit: 546.j
• Rep. character: $\chi_{546}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $36$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(546, [\chi])\).

	Total	New	Old
Modular forms	240	36	204
Cusp forms	208	36	172
Eisenstein series	32	0	32

Trace form

36 * q + 2 * q^3 + 36 * q^4 + 2 * q^7 - 18 * q^9 + 8 * q^10 + 4 * q^11 + 2 * q^12 + 2 * q^13 + 36 * q^16 + 8 * q^17 + 6 * q^19 - 2 * q^21 - 4 * q^22 - 16 * q^23 - 6 * q^25 - 4 * q^26 - 4 * q^27 + 2 * q^28 + 4 * q^29 + 20 * q^31 - 16 * q^35 - 18 * q^36 + 68 * q^37 - 4 * q^38 - 24 * q^39 + 8 * q^40 + 4 * q^41 - 6 * q^43 + 4 * q^44 + 24 * q^46 - 24 * q^47 + 2 * q^48 + 18 * q^49 - 16 * q^50 - 12 * q^51 + 2 * q^52 - 12 * q^53 + 4 * q^55 + 20 * q^57 - 8 * q^58 - 32 * q^59 + 26 * q^61 + 20 * q^62 - 4 * q^63 + 36 * q^64 + 40 * q^65 + 16 * q^66 - 16 * q^67 + 8 * q^68 + 8 * q^69 - 64 * q^70 + 44 * q^71 - 6 * q^73 + 24 * q^74 - 44 * q^75 + 6 * q^76 - 28 * q^77 - 16 * q^78 + 24 * q^79 - 18 * q^81 + 24 * q^82 - 112 * q^83 - 2 * q^84 - 4 * q^86 - 24 * q^87 - 4 * q^88 - 16 * q^89 - 16 * q^90 + 28 * q^91 - 16 * q^92 - 56 * q^93 + 40 * q^94 - 64 * q^95 - 30 * q^97 - 24 * q^98 - 8 * q^99

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.j.a	$546$	$2$	546.j	91.h	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.j.a	$2$	$0$	\(2\)	\(1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}+(2-3\zeta_{6})q^{7}+\cdots\)
546.2.j.b	$546$	$2$	546.j	91.h	$3$	$8$	$4$	$4.360$	8.0.6498455769.2	None		✓			546.2.j.b	$2$	$0$	\(-8\)	\(-4\)	\(-2\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots\)
546.2.j.c	$546$	$2$	546.j	91.h	$3$	$8$	$4$	$4.360$	8.0.447703281.1	None		✓			546.2.j.c	$2$	$0$	\(8\)	\(-4\)	\(2\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
546.2.j.d	$546$	$2$	546.j	91.h	$3$	$8$	$4$	$4.360$	8.0.447703281.1	None		✓			546.2.j.d	$2$	$0$	\(8\)	\(4\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}-\beta _{3}q^{3}+q^{4}+(2\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
546.2.j.e	$546$	$2$	546.j	91.h	$3$	$10$	$5$	$4.360$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		546.2.j.e	$2$	$0$	\(-10\)	\(5\)	\(-2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1+\beta _{5})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots\)

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

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