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

• Label: 5472.2.e
• Level: $5472$
• Weight: $2$
• Character orbit: 5472.e
• Rep. character: $\chi_{5472}(5167,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $7$
• Sturm bound: $1920$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5472.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1920\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	992	102	890
Cusp forms	928	98	830
Eisenstein series	64	4	60

Trace form

\( 98 q + O(q^{10}) \)

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.e.a	$5472$	$2$	5472.e	152.b	$2$	$2$	$2$	$43.694$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+6q^{11}+6q^{17}+(1+3\beta )q^{19}+5q^{25}+\cdots\)
5472.2.e.b	$5472$	$2$	5472.e	152.b	$2$	$4$	$4$	$43.694$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{7}-4q^{11}+\beta _{1}q^{13}+q^{17}+\cdots\)
5472.2.e.c	$5472$	$2$	5472.e	152.b	$2$	$8$	$8$	$43.694$	8.0.\(\cdots\).11	\(\Q(\sqrt{-114}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{5}-\beta _{5}q^{13}+\beta _{4}q^{19}+\beta _{6}q^{23}+\cdots\)
5472.2.e.d	$5472$	$2$	5472.e	152.b	$2$	$8$	$8$	$43.694$	8.0.207360000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{7}+\beta _{7}q^{11}+\beta _{1}q^{13}+2\beta _{7}q^{17}+\cdots\)
5472.2.e.e	$5472$	$2$	5472.e	152.b	$2$	$12$	$12$	$43.694$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{7})q^{5}-\beta _{7}q^{7}-\beta _{9}q^{11}-\beta _{11}q^{13}+\cdots\)
5472.2.e.f	$5472$	$2$	5472.e	152.b	$2$	$24$	$24$	$43.694$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
5472.2.e.g	$5472$	$2$	5472.e	152.b	$2$	$40$	$40$	$43.694$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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