Space of modular forms of level 1152, weight 2, and Character 1152.l

• Label: 1152.2.l
• Level: $1152$
• Weight: $2$
• Character orbit: 1152.l
• Rep. character: $\chi_{1152}(287,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).

	Total	New	Old
Modular forms	448	32	416
Cusp forms	320	32	288
Eisenstein series	128	0	128

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.2.l.a	$1152$	$2$	1152.l	48.k	$4$	$16$	$8$	$9.199$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{5}+\beta _{9}q^{7}+(-\beta _{2}-\beta _{14})q^{11}+\cdots\)
1152.2.l.b	$1152$	$2$	1152.l	48.k	$4$	$16$	$8$	$9.199$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{5}-\beta _{9}q^{7}+(\beta _{2}+\beta _{14})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)