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

• Label: 1152.2.f
• Level: $1152$
• Weight: $2$
• Character orbit: 1152.f
• Rep. character: $\chi_{1152}(575,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	224	16	208
Cusp forms	160	16	144
Eisenstein series	64	0	64

Trace form

\( 16 q + 16 q^{25} + 48 q^{49} + 64 q^{73}+O(q^{100}) \)

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.f.a	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	\(\Q(\zeta_{8})\)	None		✓			1152.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{5}-2\beta_{2} q^{7}+2\beta_1 q^{11}-\beta_1 q^{13}+\cdots\)
1152.2.f.b	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1152.2.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_{2} q^{5}+\beta_1 q^{13}+\beta_{3} q^{17}-3 q^{25}+\cdots\)
1152.2.f.c	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1152.2.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_{3} q^{5}-\beta_1 q^{13}-5\beta_{2} q^{17}+13 q^{25}+\cdots\)
1152.2.f.d	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	\(\Q(\zeta_{8})\)	None		✓			1152.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{5}-2\beta_{2} q^{7}+2\beta_1 q^{11}+\beta_1 q^{13}+\cdots\)

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

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