Space of modular forms of level 1716, weight 2, and Character 1716.d

• Label: 1716.2.d
• Level: $1716$
• Weight: $2$
• Character orbit: 1716.d
• Rep. character: $\chi_{1716}(989,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $672$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(672\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1716, [\chi])\).

	Total	New	Old
Modular forms	348	48	300
Cusp forms	324	48	276
Eisenstein series	24	0	24

Trace form

\( 48 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1716, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1716.2.d.a	$1716$	$2$	1716.d	33.d	$2$	$48$	$48$	$13.702$		None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1716, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \)