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

• Label: 5292.2.i
• Level: $5292$
• Weight: $2$
• Character orbit: 5292.i
• Rep. character: $\chi_{5292}(1549,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $10$
• Sturm bound: $2016$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(2016\)
Trace bound:			\(5\)
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

\( 80 q - 4 q^{5} + O(q^{10}) \)

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.i.a	$5292$	$2$	5292.i	63.h	$3$	$2$	$1$	$42.257$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{5}+3\zeta_{6}q^{11}-\zeta_{6}q^{13}+\cdots\)
5292.2.i.b	$5292$	$2$	5292.i	63.h	$3$	$2$	$1$	$42.257$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{5}+4\zeta_{6}q^{11}+3\zeta_{6}q^{13}+\cdots\)
5292.2.i.c	$5292$	$2$	5292.i	63.h	$3$	$2$	$1$	$42.257$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{5}+3\zeta_{6}q^{11}+\zeta_{6}q^{13}+\cdots\)
5292.2.i.d	$5292$	$2$	5292.i	63.h	$3$	$6$	$3$	$42.257$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}+\beta _{3})q^{5}+(-\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots\)
5292.2.i.e	$5292$	$2$	5292.i	63.h	$3$	$6$	$3$	$42.257$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{5})q^{5}+(1-2\beta _{2}-\beta _{4}-\beta _{5})q^{11}+\cdots\)
5292.2.i.f	$5292$	$2$	5292.i	63.h	$3$	$6$	$3$	$42.257$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{5})q^{5}+(1-2\beta _{2}-\beta _{4}-\beta _{5})q^{11}+\cdots\)
5292.2.i.g	$5292$	$2$	5292.i	63.h	$3$	$6$	$3$	$42.257$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}-\beta _{3})q^{5}+(-\beta _{2}-2\beta _{3})q^{11}+\cdots\)
5292.2.i.h	$5292$	$2$	5292.i	63.h	$3$	$12$	$6$	$42.257$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{6}q^{5}+(-1+\beta _{4}+\beta _{5})q^{11}+(\beta _{8}+\cdots)q^{13}+\cdots\)
5292.2.i.i	$5292$	$2$	5292.i	63.h	$3$	$14$	$7$	$42.257$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$3^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{5}+(\beta _{7}+\beta _{13})q^{11}-\beta _{11}q^{13}+\cdots\)
5292.2.i.j	$5292$	$2$	5292.i	63.h	$3$	$24$	$12$	$42.257$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(5292, [\chi]) \cong \)