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

• Label: 5472.2.f
• Level: $5472$
• Weight: $2$
• Character orbit: 5472.f
• Rep. character: $\chi_{5472}(1025,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $1920$
• Trace bound: $59$

Defining parameters

Level:	\( N \)	\(=\)	\( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5472.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1920\)
Trace bound:			\(59\)
Distinguishing \(T_p\):			\(5\), \(29\), \(59\)

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.f.a	$5472$	$2$	5472.f	57.d	$2$	$20$	$20$	$43.694$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{5}-\beta _{1}q^{7}+\beta _{7}q^{11}+(-\beta _{4}+\cdots)q^{13}+\cdots\)
5472.2.f.b	$5472$	$2$	5472.f	57.d	$2$	$20$	$20$	$43.694$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{5}+\beta _{1}q^{7}-\beta _{7}q^{11}+(-\beta _{4}+\cdots)q^{13}+\cdots\)
5472.2.f.c	$5472$	$2$	5472.f	57.d	$2$	$20$	$20$	$43.694$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{21}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{5}+\beta _{3}q^{7}+\beta _{14}q^{11}-\beta _{4}q^{13}+\cdots\)
5472.2.f.d	$5472$	$2$	5472.f	57.d	$2$	$20$	$20$	$43.694$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{21}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{5}+\beta _{3}q^{7}+\beta _{14}q^{11}+\beta _{4}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(5472, [\chi]) \cong \)