Space of modular forms of level 2592, weight 2, and Character 2592.f

• Label: 2592.2.f
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.f
• Rep. character: $\chi_{2592}(1295,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $3$
• Sturm bound: $864$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(864\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2592, [\chi])\).

	Total	New	Old
Modular forms	480	52	428
Cusp forms	384	44	340
Eisenstein series	96	8	88

Trace form

\( 44 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2592, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2592.2.f.a	$2592$	$2$	2592.f	24.f	$2$	$4$	$4$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{11}+(-2\beta _{1}-\beta _{2})q^{17}+\cdots\)
2592.2.f.b	$2592$	$2$	2592.f	24.f	$2$	$16$	$16$	$20.697$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{10}q^{7}+(\beta _{1}+\beta _{7})q^{11}+\cdots\)
2592.2.f.c	$2592$	$2$	2592.f	24.f	$2$	$24$	$24$	$20.697$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)