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

• Label: 1152.2.d
• Level: $1152$
• Weight: $2$
• Character orbit: 1152.d
• Rep. character: $\chi_{1152}(577,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	224	20	204
Cusp forms	160	20	140
Eisenstein series	64	0	64

Trace form

\( 20 q + O(q^{10}) \)

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.d.a	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{7}+iq^{11}-iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.b	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}+2iq^{13}-8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.c	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{11}-6q^{17}-3\beta q^{19}+5q^{25}+\cdots\)
1152.2.d.d	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}+iq^{13}+2q^{17}-11q^{25}+\cdots\)
1152.2.d.e	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}-2iq^{13}+8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.f	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{7}+iq^{11}+iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.g	$1152$	$2$	1152.d	8.b	$2$	$4$	$4$	$9.199$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-7q^{25}+\cdots\)
1152.2.d.h	$1152$	$2$	1152.d	8.b	$2$	$4$	$4$	$9.199$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}-2\zeta_{8}^{2}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \)