Space of modular forms of level 5472, weight 2, and Character 5472.p

• Label: 5472.2.p
• Level: $5472$
• Weight: $2$
• Character orbit: 5472.p
• Rep. character: $\chi_{5472}(3761,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $1920$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5472.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1920\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5472, [\chi])\).

	Total	New	Old
Modular forms	992	80	912
Cusp forms	928	80	848
Eisenstein series	64	0	64

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5472, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5472.2.p.a	$5472$	$2$	5472.p	456.p	$2$	$80$	$80$	$43.694$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5472, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5472, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2736, [\chi])\)\(^{\oplus 2}\)