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

• Label: 1152.3.b
• Level: $1152$
• Weight: $3$
• Character orbit: 1152.b
• Rep. character: $\chi_{1152}(703,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $10$
• Sturm bound: $576$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1152.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(576\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

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.b.a	$1152$	$3$	1152.b	8.d	$2$	$2$	$2$	$31.390$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}-3iq^{13}-30q^{17}-39q^{25}+\cdots\)
1152.3.b.b	$1152$	$3$	1152.b	8.d	$2$	$2$	$2$	$31.390$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}+4iq^{13}-2^{4}q^{17}-11q^{25}+\cdots\)
1152.3.b.c	$1152$	$3$	1152.b	8.d	$2$	$2$	$2$	$31.390$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-2}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{11}+2q^{17}-\beta q^{19}+5^{2}q^{25}+\cdots\)
1152.3.b.d	$1152$	$3$	1152.b	8.d	$2$	$2$	$2$	$31.390$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}-4iq^{13}+2^{4}q^{17}-11q^{25}+\cdots\)
1152.3.b.e	$1152$	$3$	1152.b	8.d	$2$	$4$	$4$	$31.390$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots\)
1152.3.b.f	$1152$	$3$	1152.b	8.d	$2$	$4$	$4$	$31.390$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+21q^{25}+\cdots\)
1152.3.b.g	$1152$	$3$	1152.b	8.d	$2$	$4$	$4$	$31.390$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5\zeta_{8}^{2}q^{11}+5\zeta_{8}q^{13}+\cdots\)
1152.3.b.h	$1152$	$3$	1152.b	8.d	$2$	$4$	$4$	$31.390$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{11}+\cdots\)
1152.3.b.i	$1152$	$3$	1152.b	8.d	$2$	$8$	$8$	$31.390$	8.0.157351936.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{5}q^{7}-\beta _{3}q^{11}-\beta _{2}q^{13}+\cdots\)
1152.3.b.j	$1152$	$3$	1152.b	8.d	$2$	$8$	$8$	$31.390$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{24}-\zeta_{24}^{4})q^{5}+\zeta_{24}^{2}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)