Space of modular forms of level 1116, weight 2, and Character 1116.k

• Label: 1116.2.k
• Level: $1116$
• Weight: $2$
• Character orbit: 1116.k
• Rep. character: $\chi_{1116}(769,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1116.k (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 279 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1116, [\chi])\).

	Total	New	Old
Modular forms	396	64	332
Cusp forms	372	64	308
Eisenstein series	24	0	24

Trace form

\( 64 q - 4 q^{3} + q^{5} - q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1116, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1116.2.k.a	$1116$	$2$	1116.k	279.e	$3$	$2$	$1$	$8.911$	\(\Q(\sqrt{-3}) \)	None		✓			1116.2.k.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\)
1116.2.k.b	$1116$	$2$	1116.k	279.e	$3$	$62$	$31$	$8.911$		None		✓	✓		1116.2.k.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1116, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1116, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)