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

• Label: 1152.5.h
• Level: $1152$
• Weight: $5$
• Character orbit: 1152.h
• Rep. character: $\chi_{1152}(449,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $960$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	1152.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(960\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	800	64	736
Cusp forms	736	64	672
Eisenstein series	64	0	64

Trace form

\( 64 q + 8000 q^{25} + 9920 q^{49} - 29440 q^{73} - 22528 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.5.h.a	$1152$	$5$	1152.h	24.h	$2$	$4$	$4$	$119.082$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1152.5.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+17\beta_{3} q^{5}-119\beta_1 q^{13}-401\beta_{2} q^{17}+\cdots\)
1152.5.h.b	$1152$	$5$	1152.h	24.h	$2$	$4$	$4$	$119.082$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1152.5.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-31\beta_{3} q^{5}+119\beta_1 q^{13}-79\beta_{2} q^{17}+\cdots\)
1152.5.h.c	$1152$	$5$	1152.h	24.h	$2$	$8$	$8$	$119.082$	8.0.\(\cdots\).276	None		✓			1152.5.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{2}q^{7}+(-40-\beta _{3})q^{11}+\cdots\)
1152.5.h.d	$1152$	$5$	1152.h	24.h	$2$	$8$	$8$	$119.082$	8.0.\(\cdots\).9	None		✓			1152.5.h.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{2}q^{5}+\beta _{6}q^{7}+\beta _{5}q^{11}+119\beta _{1}q^{13}+\cdots\)
1152.5.h.e	$1152$	$5$	1152.h	24.h	$2$	$8$	$8$	$119.082$	8.0.\(\cdots\).276	None		✓			1152.5.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+(40+\beta _{3})q^{11}-\beta _{5}q^{13}+\cdots\)
1152.5.h.f	$1152$	$5$	1152.h	24.h	$2$	$16$	$16$	$119.082$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1152.5.h.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{64}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{8}+\beta _{9})q^{5}-\beta _{12}q^{7}-\beta _{3}q^{11}+\cdots\)
1152.5.h.g	$1152$	$5$	1152.h	24.h	$2$	$16$	$16$	$119.082$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1152.5.h.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{60}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{5}-\beta _{12}q^{7}+\beta _{1}q^{11}+\beta _{5}q^{13}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(1152, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)