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

• Label: 1152.3.e
• Level: $1152$
• Weight: $3$
• Character orbit: 1152.e
• Rep. character: $\chi_{1152}(1025,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $8$
• Sturm bound: $576$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1152.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(576\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	416	32	384
Cusp forms	352	32	320
Eisenstein series	64	0	64

Trace form

\( 32 q - 160 q^{25} + 96 q^{49} + 640 q^{73} - 768 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.3.e.a	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		✓			1152.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}-2q^{7}+(6\beta _{1}-2\beta _{3})q^{11}+\cdots\)
1152.3.e.b	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			1152.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(-2+2\beta _{3})q^{7}+\cdots\)
1152.3.e.c	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		✓			1152.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}-2q^{7}+(6\beta _{1}-2\beta _{3})q^{11}+\cdots\)
1152.3.e.d	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			1152.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(-2+2\beta _{3})q^{7}+\cdots\)
1152.3.e.e	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		✓			1152.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+2q^{7}+(-6\beta _{1}+2\beta _{3})q^{11}+\cdots\)
1152.3.e.f	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			1152.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(2-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
1152.3.e.g	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		✓			1152.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+2q^{7}+(-6\beta _{1}+2\beta _{3})q^{11}+\cdots\)
1152.3.e.h	$1152$	$3$	1152.e	3.b	$2$	$4$	$4$	$31.390$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			1152.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(2-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)