Space of modular forms of level 2592, weight 1, and Character 2592.e

• Label: 2592.1.e
• Level: $2592$
• Weight: $1$
• Character orbit: 2592.e
• Rep. character: $\chi_{2592}(161,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $432$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2592.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(432\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2592, [\chi])\).

	Total	New	Old
Modular forms	70	4	66
Cusp forms	22	4	18
Eisenstein series	48	0	48

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 4 q^{25} + 4 q^{37} - 4 q^{49} - 4 q^{61} - 4 q^{85}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2592, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2592.1.e.a	$2592$	$1$	2592.e	3.b	$2$	$4$	$4$	$1.294$	\(\Q(\sqrt{-2}, \sqrt{3})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	2592.1.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{5}-\beta _{2}q^{13}-\beta _{3}q^{17}+(-1+\cdots)q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2592, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2592, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)