Space of modular forms of level 1152, weight 3, and Character 1152.g

• Label: 1152.3.g
• Level: $1152$
• Weight: $3$
• Character orbit: 1152.g
• Rep. character: $\chi_{1152}(127,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1152.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1152, [\chi])\).

	Total	New	Old
Modular forms	416	40	376
Cusp forms	352	40	312
Eisenstein series	64	0	64

Trace form

\( 40 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.3.g.a	$1152$	$3$	1152.g	4.b	$2$	$4$	$4$	$31.390$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\zeta_{8}^{3})q^{5}+(-\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots\)
1152.3.g.b	$1152$	$3$	1152.g	4.b	$2$	$4$	$4$	$31.390$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
1152.3.g.c	$1152$	$3$	1152.g	4.b	$2$	$8$	$8$	$31.390$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\zeta_{24})q^{5}-\zeta_{24}^{6}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
1152.3.g.d	$1152$	$3$	1152.g	4.b	$2$	$8$	$8$	$31.390$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{5}q^{7}+\beta _{1}q^{11}+(-6+\beta _{7})q^{13}+\cdots\)
1152.3.g.e	$1152$	$3$	1152.g	4.b	$2$	$8$	$8$	$31.390$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{5}q^{7}+\beta _{1}q^{11}+(6-\beta _{7})q^{13}+\cdots\)
1152.3.g.f	$1152$	$3$	1152.g	4.b	$2$	$8$	$8$	$31.390$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\zeta_{24}^{2})q^{5}-\zeta_{24}^{4}q^{7}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)