Space of modular forms of level 2432, weight 1, and Character 2432.e

• Label: 2432.1.e
• Level: $2432$
• Weight: $1$
• Character orbit: 2432.e
• Rep. character: $\chi_{2432}(1025,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $320$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2432 = 2^{7} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2432.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(320\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2432, [\chi])\).

	Total	New	Old
Modular forms	38	8	30
Cusp forms	22	8	14
Eisenstein series	16	0	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

\( 8 q - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2432, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2432.1.e.a	$2432$	$1$	2432.e	19.b	$2$	$2$	$2$	$1.214$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$1$		\(q-\beta q^{3}-q^{5}-q^{7}-q^{9}-q^{11}+\beta q^{15}+\cdots\)
2432.1.e.b	$2432$	$1$	2432.e	19.b	$2$	$2$	$2$	$1.214$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$1$		\(q-\beta q^{3}-q^{5}+q^{7}-q^{9}+q^{11}+\beta q^{15}+\cdots\)
2432.1.e.c	$2432$	$1$	2432.e	19.b	$2$	$2$	$2$	$1.214$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$1$		\(q-\beta q^{3}+q^{5}-q^{7}-q^{9}+q^{11}-\beta q^{15}+\cdots\)
2432.1.e.d	$2432$	$1$	2432.e	19.b	$2$	$2$	$2$	$1.214$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$1$		\(q-\beta q^{3}+q^{5}+q^{7}-q^{9}-q^{11}-\beta q^{15}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2432, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2432, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1216, [\chi])\)\(^{\oplus 2}\)