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

• Label: 5328.2.l
• Level: $5328$
• Weight: $2$
• Character orbit: 5328.l
• Rep. character: $\chi_{5328}(5327,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $6$
• Sturm bound: $1824$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5328.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 444 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1824\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	936	76	860
Cusp forms	888	76	812
Eisenstein series	48	0	48

Trace form

\( 76 q + 76 q^{25} - 20 q^{37} - 92 q^{49} - 16 q^{73} + 120 q^{85}+O(q^{100}) \)

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.l.a	$5328$	$2$	5328.l	444.g	$2$	$4$	$4$	$42.544$	\(\Q(\sqrt{-2}, \sqrt{37})\)	\(\Q(\sqrt{-37}) \)		✓			5328.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\beta _{1})q^{19}-\beta _{2}q^{23}-5q^{25}+\cdots\)
5328.2.l.b	$5328$	$2$	5328.l	444.g	$2$	$4$	$4$	$42.544$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			5328.2.l.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_{3} q^{5}+\beta_1 q^{13}-\beta_{3} q^{17}+13 q^{25}+\cdots\)
5328.2.l.c	$5328$	$2$	5328.l	444.g	$2$	$4$	$4$	$42.544$	\(\Q(\sqrt{-2}, \sqrt{37})\)	\(\Q(\sqrt{-37}) \)		✓			5328.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta _{1})q^{19}-\beta _{2}q^{23}-5q^{25}+(5+\cdots)q^{31}+\cdots\)
5328.2.l.d	$5328$	$2$	5328.l	444.g	$2$	$8$	$8$	$42.544$	8.0.4956160000.2	None		✓			5328.2.l.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-\beta _{6}q^{7}+2\beta _{2}q^{11}+\beta _{5}q^{13}+\cdots\)
5328.2.l.e	$5328$	$2$	5328.l	444.g	$2$	$8$	$8$	$42.544$	8.0.4956160000.2	None		✓			5328.2.l.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{6}q^{7}-2\beta _{2}q^{11}+\beta _{5}q^{13}+\cdots\)
5328.2.l.f	$5328$	$2$	5328.l	444.g	$2$	$48$	$48$	$42.544$		None		✓	✓		5328.2.l.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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