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

• Label: 1716.2.p
• Level: $1716$
• Weight: $2$
• Character orbit: 1716.p
• Rep. character: $\chi_{1716}(857,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• 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.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 429 \)
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	56	292
Cusp forms	324	56	268
Eisenstein series	24	0	24

Trace form

\( 56 q - 8 q^{9} + O(q^{10}) \)

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	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1716.2.p.a	$1716$	$2$	1716.p	429.e	$2$	$56$	$56$	$13.702$		None		✓	1716.2.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(858, [\chi])\)\(^{\oplus 2}\)