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

• Label: 1152.2.v
• Level: $1152$
• Weight: $2$
• Character orbit: 1152.v
• Rep. character: $\chi_{1152}(145,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $76$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.v (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	832	84	748
Cusp forms	704	76	628
Eisenstein series	128	8	120

Trace form

\( 76 q + 4 q^{5} + 4 q^{7} + O(q^{10}) \)

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.v.a	$1152$	$2$	1152.v	32.g	$8$	$4$	$1$	$9.199$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1+\zeta_{8}+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1152.2.v.b	$1152$	$2$	1152.v	32.g	$8$	$8$	$2$	$9.199$	8.0.18939904.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\beta _{4}-\beta _{7})q^{5}+(1-\beta _{1}-\beta _{3}+\beta _{7})q^{7}+\cdots\)
1152.2.v.c	$1152$	$2$	1152.v	32.g	$8$	$32$	$8$	$9.199$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
1152.2.v.d	$1152$	$2$	1152.v	32.g	$8$	$32$	$8$	$9.199$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)