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

• Label: 5472.2.g
• Level: $5472$
• Weight: $2$
• Character orbit: 5472.g
• Rep. character: $\chi_{5472}(2737,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $5$
• Sturm bound: $1920$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5472.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1920\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	992	90	902
Cusp forms	928	90	838
Eisenstein series	64	0	64

Trace form

\( 90 q + 4 q^{7} + O(q^{10}) \)

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.g.a	$5472$	$2$	5472.g	8.b	$2$	$2$	$2$	$43.694$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{7}+4iq^{11}-2iq^{13}-2q^{17}+\cdots\)
5472.2.g.b	$5472$	$2$	5472.g	8.b	$2$	$16$	$16$	$43.694$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{12})q^{7}+\beta _{8}q^{11}+\cdots\)
5472.2.g.c	$5472$	$2$	5472.g	8.b	$2$	$18$	$18$	$43.694$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}+(-1-\beta _{12})q^{7}-\beta _{6}q^{11}+\cdots\)
5472.2.g.d	$5472$	$2$	5472.g	8.b	$2$	$18$	$18$	$43.694$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{14}q^{5}+(1-\beta _{15})q^{7}+(-\beta _{3}-\beta _{7}+\cdots)q^{11}+\cdots\)
5472.2.g.e	$5472$	$2$	5472.g	8.b	$2$	$36$	$36$	$43.694$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

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

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