Space of modular forms of level 5292, weight 2, and Character 5292.x

• Label: 5292.2.x
• Level: $5292$
• Weight: $2$
• Character orbit: 5292.x
• Rep. character: $\chi_{5292}(881,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $2016$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.x (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(2016\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5292, [\chi])\).

	Total	New	Old
Modular forms	2160	80	2080
Cusp forms	1872	80	1792
Eisenstein series	288	0	288

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5292, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5292.2.x.a	$5292$	$2$	5292.x	63.o	$6$	$16$	$8$	$42.257$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{5}+\beta _{15}q^{11}+(-\beta _{1}-\beta _{9}-\beta _{13}+\cdots)q^{13}+\cdots\)
5292.2.x.b	$5292$	$2$	5292.x	63.o	$6$	$16$	$8$	$42.257$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{11}q^{5}+(\beta _{2}-\beta _{3}+\beta _{4}-\beta _{6}-\beta _{10}+\cdots)q^{11}+\cdots\)
5292.2.x.c	$5292$	$2$	5292.x	63.o	$6$	$48$	$24$	$42.257$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5292, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5292, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2646, [\chi])\)\(^{\oplus 2}\)