Space of modular forms of level 486, weight 2, and trivial character

• Label: 486.2.a
• Level: $486$
• Weight: $2$
• Character orbit: 486.a
• Rep. character: $\chi_{486}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• 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.a (trivial)
Character field:			\(\Q\)
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 \(M_{2}(\Gamma_0(486))\).

	Total	New	Old
Modular forms	99	12	87
Cusp forms	64	12	52
Eisenstein series	35	0	35

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(20\)	\(2\)	\(18\)		\(12\)	\(2\)	\(10\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)		\(29\)	\(4\)	\(25\)		\(20\)	\(4\)	\(16\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)		\(25\)	\(5\)	\(20\)		\(16\)	\(5\)	\(11\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)		\(25\)	\(1\)	\(24\)		\(16\)	\(1\)	\(15\)		\(9\)	\(0\)	\(9\)
Plus space		\(+\)		\(45\)	\(3\)	\(42\)		\(28\)	\(3\)	\(25\)		\(17\)	\(0\)	\(17\)
Minus space		\(-\)		\(54\)	\(9\)	\(45\)		\(36\)	\(9\)	\(27\)		\(18\)	\(0\)	\(18\)

Trace form

12 * q + 12 * q^4 + 6 * q^7 + 6 * q^13 + 12 * q^16 + 6 * q^19 + 12 * q^25 + 6 * q^28 + 6 * q^31 + 6 * q^37 + 6 * q^43 + 18 * q^49 + 6 * q^52 + 18 * q^55 + 18 * q^58 - 48 * q^61 + 12 * q^64 - 48 * q^67 + 18 * q^70 - 48 * q^73 + 6 * q^76 + 24 * q^79 - 72 * q^82 - 72 * q^85 - 42 * q^91 - 66 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(486))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
486.2.a.a	$486$	$2$	486.a	1.a	$1$	$1$	$1$	$3.881$	\(\Q\)	None	✓	✓			486.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}+2q^{7}-q^{8}+3q^{10}+\cdots\)
486.2.a.b	$486$	$2$	486.a	1.a	$1$	$1$	$1$	$3.881$	\(\Q\)	None	✓	✓			486.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}-q^{13}+\cdots\)
486.2.a.c	$486$	$2$	486.a	1.a	$1$	$1$	$1$	$3.881$	\(\Q\)	None	✓	✓			486.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots\)
486.2.a.d	$486$	$2$	486.a	1.a	$1$	$1$	$1$	$3.881$	\(\Q\)	None	✓	✓	✓	✓	486.2.a.c	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-4q^{7}+q^{8}-3q^{10}+\cdots\)
486.2.a.e	$486$	$2$	486.a	1.a	$1$	$1$	$1$	$3.881$	\(\Q\)	None	✓	✓			486.2.a.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}-q^{13}+\cdots\)
486.2.a.f	$486$	$2$	486.a	1.a	$1$	$1$	$1$	$3.881$	\(\Q\)	None	✓	✓			486.2.a.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+2q^{7}+q^{8}+3q^{10}+\cdots\)
486.2.a.g	$486$	$2$	486.a	1.a	$1$	$3$	$3$	$3.881$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		486.2.a.g	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)		$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
486.2.a.h	$486$	$2$	486.a	1.a	$1$	$3$	$3$	$3.881$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		486.2.a.g	$1$	$0$	\(3\)	\(0\)	\(0\)	\(6\)		$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(486))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(486)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 2}\)