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

• Label: 2592.1.b
• Level: $2592$
• Weight: $1$
• Character orbit: 2592.b
• Rep. character: $\chi_{2592}(1135,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $432$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2592.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(432\)
Trace bound:			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	56	6	50
Cusp forms	8	2	6
Eisenstein series	48	4	44

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2592.1.b.a	$2592$	$1$	2592.b	8.d	$2$	$1$	$1$	$1.294$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{11}+q^{17}+q^{19}+q^{25}+q^{41}+\cdots\)
2592.1.b.b	$2592$	$1$	2592.b	8.d	$2$	$1$	$1$	$1.294$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{11}-q^{17}+q^{19}+q^{25}-q^{41}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2592, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)