Space of modular forms of level 486, weight 2, and Character 486.c

• Label: 486.2.c
• Level: $486$
• Weight: $2$
• Character orbit: 486.c
• Rep. character: $\chi_{486}(163,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $8$
• Sturm bound: $162$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(162\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(486, [\chi])\).

	Total	New	Old
Modular forms	198	24	174
Cusp forms	126	24	102
Eisenstein series	72	0	72

Trace form

24 * q - 12 * q^4 - 6 * q^7 - 6 * q^13 - 12 * q^16 + 12 * q^19 - 12 * q^25 + 12 * q^28 - 6 * q^31 + 12 * q^37 - 6 * q^43 - 18 * q^49 - 6 * q^52 + 36 * q^55 - 18 * q^58 + 48 * q^61 + 24 * q^64 + 48 * q^67 - 18 * q^70 - 96 * q^73 - 6 * q^76 - 24 * q^79 - 144 * q^82 + 72 * q^85 - 84 * q^91 + 66 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(486, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
486.2.c.a	$486$	$2$	486.c	9.c	$3$	$2$	$1$	$3.881$	\(\Q(\sqrt{-3}) \)	None		✓			486.2.a.a	$2$	$1$	\(-1\)	\(0\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
486.2.c.b	$486$	$2$	486.c	9.c	$3$	$2$	$1$	$3.881$	\(\Q(\sqrt{-3}) \)	None		✓			486.2.a.b	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots\)
486.2.c.c	$486$	$2$	486.c	9.c	$3$	$2$	$1$	$3.881$	\(\Q(\sqrt{-3}) \)	None		✓			486.2.a.c	$2$	$0$	\(-1\)	\(0\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
486.2.c.d	$486$	$2$	486.c	9.c	$3$	$2$	$1$	$3.881$	\(\Q(\sqrt{-3}) \)	None		✓			486.2.a.c	$2$	$0$	\(1\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
486.2.c.e	$486$	$2$	486.c	9.c	$3$	$2$	$1$	$3.881$	\(\Q(\sqrt{-3}) \)	None		✓			486.2.a.b	$2$	$0$	\(1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots\)
486.2.c.f	$486$	$2$	486.c	9.c	$3$	$2$	$1$	$3.881$	\(\Q(\sqrt{-3}) \)	None		✓			486.2.a.a	$2$	$0$	\(1\)	\(0\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
486.2.c.g	$486$	$2$	486.c	9.c	$3$	$6$	$3$	$3.881$	\(\Q(\zeta_{18})\)	None		✓			486.2.a.g	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-6\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_1 q^{2}+(\beta_1-1)q^{4}+(\beta_{5}-\beta_{4}+\cdots-\beta_{2})q^{5}+\cdots\)
486.2.c.h	$486$	$2$	486.c	9.c	$3$	$6$	$3$	$3.881$	\(\Q(\zeta_{18})\)	None		✓			486.2.a.g	$2$	$0$	\(3\)	\(0\)	\(0\)	\(-6\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta_1 q^{2}+(\beta_1-1)q^{4}+\beta_{4} q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(486, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(486, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 2}\)