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

• Label: 546.2.q
• Level: $546$
• Weight: $2$
• Character orbit: 546.q
• Rep. character: $\chi_{546}(251,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $10$
• 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.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	240	72	168
Cusp forms	208	72	136
Eisenstein series	32	0	32

Trace form

72 * q - 36 * q^4 - 4 * q^9 - 12 * q^15 - 36 * q^16 - 56 * q^25 - 16 * q^30 - 4 * q^36 + 48 * q^39 + 16 * q^42 - 20 * q^43 + 12 * q^46 - 12 * q^49 - 48 * q^51 + 96 * q^63 + 72 * q^64 - 84 * q^67 + 12 * q^72 - 44 * q^78 + 16 * q^79 + 56 * q^81 - 120 * q^85 + 32 * q^91 + 48 * q^93

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.q.a	$546$	$2$	546.q	273.u	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.q.a	$2$	$0$	\(-1\)	\(-3\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.b	$546$	$2$	546.q	273.u	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.q.a	$2$	$0$	\(-1\)	\(3\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.c	$546$	$2$	546.q	273.u	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.q.a	$2$	$0$	\(1\)	\(-3\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.d	$546$	$2$	546.q	273.u	$6$	$2$	$1$	$4.360$	\(\Q(\sqrt{-3}) \)	None		✓			546.2.q.a	$2$	$0$	\(1\)	\(3\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.e	$546$	$2$	546.q	273.u	$6$	$4$	$2$	$4.360$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			546.2.q.e	$2$	$0$	\(-2\)	\(-1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
546.2.q.f	$546$	$2$	546.q	273.u	$6$	$4$	$2$	$4.360$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			546.2.q.e	$2$	$0$	\(-2\)	\(1\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
546.2.q.g	$546$	$2$	546.q	273.u	$6$	$4$	$2$	$4.360$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			546.2.q.e	$2$	$0$	\(2\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
546.2.q.h	$546$	$2$	546.q	273.u	$6$	$4$	$2$	$4.360$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			546.2.q.e	$2$	$0$	\(2\)	\(2\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
546.2.q.i	$546$	$2$	546.q	273.u	$6$	$24$	$12$	$4.360$		None		✓			546.2.q.i	$4$	$0$	\(-12\)	\(0\)	\(0\)	\(-18\)		$\mathrm{SU}(2)[C_{6}]$
546.2.q.j	$546$	$2$	546.q	273.u	$6$	$24$	$12$	$4.360$		None		✓			546.2.q.i	$4$	$0$	\(12\)	\(0\)	\(0\)	\(-18\)		$\mathrm{SU}(2)[C_{6}]$

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

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