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

• Label: 546.2.i
• Level: $546$
• Weight: $2$
• Character orbit: 546.i
• Rep. character: $\chi_{546}(79,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $11$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	240	32	208
Cusp forms	208	32	176
Eisenstein series	32	0	32

Trace form

32 * q - 16 * q^4 + 8 * q^5 + 8 * q^6 - 12 * q^7 - 16 * q^9 + 4 * q^10 + 8 * q^11 + 8 * q^13 - 4 * q^14 - 8 * q^15 - 16 * q^16 - 12 * q^17 - 8 * q^19 - 16 * q^20 - 4 * q^24 - 20 * q^25 + 12 * q^28 - 24 * q^29 - 8 * q^30 + 20 * q^31 - 4 * q^33 + 16 * q^34 - 24 * q^35 + 32 * q^36 + 20 * q^38 + 4 * q^40 + 64 * q^41 + 12 * q^42 - 32 * q^43 + 8 * q^44 + 8 * q^45 - 8 * q^46 + 24 * q^47 - 16 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^52 + 12 * q^53 - 4 * q^54 + 8 * q^55 - 4 * q^56 + 16 * q^57 + 12 * q^58 + 4 * q^60 - 4 * q^61 + 16 * q^62 + 32 * q^64 - 8 * q^65 + 16 * q^67 - 12 * q^68 - 32 * q^69 - 12 * q^70 - 16 * q^73 + 16 * q^76 - 8 * q^77 + 12 * q^79 + 8 * q^80 - 16 * q^81 - 32 * q^85 - 16 * q^86 + 4 * q^87 - 16 * q^89 - 8 * q^90 + 16 * q^91 - 8 * q^93 + 4 * q^94 - 24 * q^95 - 4 * q^96 - 40 * q^97 - 48 * q^98 - 16 * 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.i.a	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.i.a	$2$	$1$	\(-1\)	\(-1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.b	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.i.b	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.c	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.i.c	$2$	$0$	\(-1\)	\(-1\)	\(4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.d	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.i.d	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.e	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.i.e	$2$	$0$	\(1\)	\(-1\)	\(2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.f	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.i.f	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.g	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.i.g	$2$	$0$	\(1\)	\(1\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.h	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			546.2.i.h	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
546.2.i.i	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			546.2.i.i	$2$	$0$	\(-2\)	\(2\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
546.2.i.j	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		✓			546.2.i.j	$2$	$0$	\(2\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.i.k	$546$	$2$	546.i	7.c	$3$	$6$	$3$	$4.360$	6.0.21870000.1	None		✓	✓		546.2.i.k	$2$	$0$	\(3\)	\(3\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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