Space of modular forms of level 1152, weight 5, and Character 1152.b

• Label: 1152.5.b
• Level: $1152$
• Weight: $5$
• Character orbit: 1152.b
• Rep. character: $\chi_{1152}(703,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $14$
• Sturm bound: $960$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	1152.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(960\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(1152, [\chi])\).

	Total	New	Old
Modular forms	800	80	720
Cusp forms	736	80	656
Eisenstein series	64	0	64

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(1152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.5.b.a	$1152$	$5$	1152.b	8.d	$2$	$2$	$2$	$119.082$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-2}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+7\beta q^{11}-574q^{17}+17\beta q^{19}+5^{4}q^{25}+\cdots\)
1152.5.b.b	$1152$	$5$	1152.b	8.d	$2$	$2$	$2$	$119.082$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+7iq^{5}-120iq^{13}-480q^{17}+429q^{25}+\cdots\)
1152.5.b.c	$1152$	$5$	1152.b	8.d	$2$	$2$	$2$	$119.082$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}+5iq^{13}+322q^{17}-1679q^{25}+\cdots\)
1152.5.b.d	$1152$	$5$	1152.b	8.d	$2$	$2$	$2$	$119.082$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+7iq^{5}+120iq^{13}+480q^{17}+429q^{25}+\cdots\)
1152.5.b.e	$1152$	$5$	1152.b	8.d	$2$	$4$	$4$	$119.082$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{11}+\cdots\)
1152.5.b.f	$1152$	$5$	1152.b	8.d	$2$	$4$	$4$	$119.082$	\(\Q(\sqrt{-2}, \sqrt{-17})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{2}q^{7}+\beta _{1}q^{11}+4\beta _{3}q^{13}+\cdots\)
1152.5.b.g	$1152$	$5$	1152.b	8.d	$2$	$4$	$4$	$119.082$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-23\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}-1491q^{25}+\cdots\)
1152.5.b.h	$1152$	$5$	1152.b	8.d	$2$	$4$	$4$	$119.082$	\(\Q(\sqrt{-2}, \sqrt{-17})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{2}q^{7}+\beta _{1}q^{11}-4\beta _{3}q^{13}+\cdots\)
1152.5.b.i	$1152$	$5$	1152.b	8.d	$2$	$4$	$4$	$119.082$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{3}q^{7}-11\beta _{2}q^{11}-3^{3}\beta _{1}q^{13}+\cdots\)
1152.5.b.j	$1152$	$5$	1152.b	8.d	$2$	$4$	$4$	$119.082$	\(\Q(\sqrt{3}, \sqrt{-19})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-\beta _{3}q^{7}+13\beta _{1}q^{11}-2\beta _{2}q^{13}+\cdots\)
1152.5.b.k	$1152$	$5$	1152.b	8.d	$2$	$8$	$8$	$119.082$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(\beta _{4}+\beta _{5}+\cdots)q^{11}+\cdots\)
1152.5.b.l	$1152$	$5$	1152.b	8.d	$2$	$8$	$8$	$119.082$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{38}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{4}q^{7}+(\beta _{2}+\beta _{5})q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
1152.5.b.m	$1152$	$5$	1152.b	8.d	$2$	$16$	$16$	$119.082$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{88}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{11}q^{5}+\beta _{3}q^{7}+(2\beta _{5}+\beta _{9})q^{11}+\cdots\)
1152.5.b.n	$1152$	$5$	1152.b	8.d	$2$	$16$	$16$	$119.082$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{92}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{8}q^{7}-\beta _{7}q^{11}+\beta _{6}q^{13}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

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