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

• Label: 5292.2.f
• Level: $5292$
• Weight: $2$
• Character orbit: 5292.f
• Rep. character: $\chi_{5292}(2645,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $7$
• Sturm bound: $2016$
• Trace bound: $37$

Defining parameters

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(2016\)
Trace bound:			\(37\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	1080	54	1026
Cusp forms	936	54	882
Eisenstein series	144	0	144

Trace form

\( 54 q + O(q^{10}) \)

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.f.a	$5292$	$2$	5292.f	21.c	$2$	$2$	$2$	$42.257$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-3\zeta_{6}q^{13}+2\zeta_{6}q^{19}-5q^{25}+5\zeta_{6}q^{31}+\cdots\)
5292.2.f.b	$5292$	$2$	5292.f	21.c	$2$	$2$	$2$	$42.257$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{13}-2\zeta_{6}q^{19}-5q^{25}-\zeta_{6}q^{31}+\cdots\)
5292.2.f.c	$5292$	$2$	5292.f	21.c	$2$	$2$	$2$	$42.257$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-4\zeta_{6}q^{13}+5\zeta_{6}q^{19}-5q^{25}-5\zeta_{6}q^{31}+\cdots\)
5292.2.f.d	$5292$	$2$	5292.f	21.c	$2$	$4$	$4$	$42.257$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-2\beta _{2}q^{13}-\beta _{1}q^{17}+\beta _{2}q^{19}+\cdots\)
5292.2.f.e	$5292$	$2$	5292.f	21.c	$2$	$12$	$12$	$42.257$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{7}q^{11}+(-\beta _{10}-\beta _{11})q^{13}+\cdots\)
5292.2.f.f	$5292$	$2$	5292.f	21.c	$2$	$16$	$16$	$42.257$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{5}+(\beta _{14}-\beta _{15})q^{11}+(\beta _{2}-\beta _{7}+\cdots)q^{13}+\cdots\)
5292.2.f.g	$5292$	$2$	5292.f	21.c	$2$	$16$	$16$	$42.257$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{11}q^{11}+\beta _{15}q^{13}-\beta _{2}q^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(5292, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2646, [\chi])\)\(^{\oplus 2}\)