Space of modular forms of level 5328, weight 2, and Character 5328.e

• Label: 5328.2.e
• Level: $5328$
• Weight: $2$
• Character orbit: 5328.e
• Rep. character: $\chi_{5328}(2591,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $7$
• Sturm bound: $1824$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5328.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1824\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5328, [\chi])\).

	Total	New	Old
Modular forms	936	72	864
Cusp forms	888	72	816
Eisenstein series	48	0	48

Trace form

\( 72 q - 24 q^{25} - 120 q^{49} - 48 q^{73} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5328, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5328.2.e.a	$5328$	$2$	5328.e	12.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-2}) \)	None		✓			5328.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-4q^{11}-\beta q^{17}-2\beta q^{19}+\cdots\)
5328.2.e.b	$5328$	$2$	5328.e	12.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-2}) \)	None		✓			5328.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+4q^{11}-\beta q^{17}+2\beta q^{19}+\cdots\)
5328.2.e.c	$5328$	$2$	5328.e	12.b	$2$	$4$	$4$	$42.544$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓			5328.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{5}+2\beta _{2}q^{11}-6q^{13}-2\beta _{1}q^{17}+\cdots\)
5328.2.e.d	$5328$	$2$	5328.e	12.b	$2$	$4$	$4$	$42.544$	\(\Q(\zeta_{8})\)	None		✓			5328.2.e.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta_1 q^{7}+2\beta_{3} q^{11}+6 q^{13}+4\beta_{2} q^{17}+\cdots\)
5328.2.e.e	$5328$	$2$	5328.e	12.b	$2$	$12$	$12$	$42.544$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			5328.2.e.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{5}+\beta _{2}q^{7}+(-1+\beta _{1})q^{13}+\cdots\)
5328.2.e.f	$5328$	$2$	5328.e	12.b	$2$	$24$	$24$	$42.544$		None		✓			5328.2.e.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
5328.2.e.g	$5328$	$2$	5328.e	12.b	$2$	$24$	$24$	$42.544$		None		✓			5328.2.e.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5328, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5328, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1332, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1776, [\chi])\)\(^{\oplus 2}\)