Space of modular forms of level 1152, weight 2, and Character 1152.r

• Label: 1152.2.r
• Level: $1152$
• Weight: $2$
• Character orbit: 1152.r
• Rep. character: $\chi_{1152}(193,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).

	Total	New	Old
Modular forms	416	96	320
Cusp forms	352	96	256
Eisenstein series	64	0	64

Trace form

\( 96 q + 48 q^{25} - 32 q^{33} + 16 q^{41} - 48 q^{49} - 16 q^{57} - 16 q^{81} + 64 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.2.r.a	$1152$	$2$	1152.r	72.n	$6$	$4$	$2$	$9.199$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		✓			1152.2.r.a	$4$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(1+2\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
1152.2.r.b	$1152$	$2$	1152.r	72.n	$6$	$4$	$2$	$9.199$	\(\Q(\zeta_{12})\)	None		✓			1152.2.r.b	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}-4\zeta_{12}^{2}q^{7}+\cdots\)
1152.2.r.c	$1152$	$2$	1152.r	72.n	$6$	$4$	$2$	$9.199$	\(\Q(\zeta_{12})\)	None		✓			1152.2.r.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+4\zeta_{12}^{2}q^{7}+\cdots\)
1152.2.r.d	$1152$	$2$	1152.r	72.n	$6$	$4$	$2$	$9.199$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		✓			1152.2.r.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
1152.2.r.e	$1152$	$2$	1152.r	72.n	$6$	$16$	$8$	$9.199$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1152.2.r.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{5}-\beta _{8})q^{3}+\beta _{10}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1152.2.r.f	$1152$	$2$	1152.r	72.n	$6$	$16$	$8$	$9.199$	16.0.\(\cdots\).9	None		✓			1152.2.r.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{3}+(\beta _{4}+\beta _{7})q^{5}+(\beta _{6}+\beta _{11}+\cdots)q^{7}+\cdots\)
1152.2.r.g	$1152$	$2$	1152.r	72.n	$6$	$24$	$12$	$9.199$		None		✓			1152.2.r.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1152.2.r.h	$1152$	$2$	1152.r	72.n	$6$	$24$	$12$	$9.199$		None		✓			1152.2.r.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)