Space of modular forms of level 1152, weight 4, and Character 1152.d

• Label: 1152.4.d
• Level: $1152$
• Weight: $4$
• Character orbit: 1152.d
• Rep. character: $\chi_{1152}(577,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $17$
• Sturm bound: $768$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1152.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(768\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1152, [\chi])\).

	Total	New	Old
Modular forms	608	60	548
Cusp forms	544	60	484
Eisenstein series	64	0	64

Trace form

\( 60 q - 104 q^{17} - 1588 q^{25} - 392 q^{41} + 1500 q^{49} - 416 q^{65} + 24 q^{73} - 1960 q^{89} + 2008 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1152, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.4.d.a	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-1}) \)	None					128.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-64\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{5}-32 q^{7}-2\beta q^{11}-5\beta q^{13}+\cdots\)
1152.4.d.b	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-1}) \)	None					384.4.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}-12 q^{7}-3\beta q^{11}-5\beta q^{13}+\cdots\)
1152.4.d.c	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			1152.4.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+11\beta q^{5}+46\beta q^{13}-104 q^{17}+\cdots\)
1152.4.d.d	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					128.4.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-23\beta q^{13}-94 q^{17}+109 q^{25}+\cdots\)
1152.4.d.e	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)					128.4.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-5^{2}\beta q^{11}+90q^{17}+45\beta q^{19}+5^{3}q^{25}+\cdots\)
1152.4.d.f	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			1152.4.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+11\beta q^{5}-46\beta q^{13}+104 q^{17}+\cdots\)
1152.4.d.g	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-1}) \)	None					384.4.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(24\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+12 q^{7}+3\beta q^{11}-5\beta q^{13}+\cdots\)
1152.4.d.h	$1152$	$4$	1152.d	8.b	$2$	$2$	$2$	$67.970$	\(\Q(\sqrt{-1}) \)	None					128.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(64\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{5}+32 q^{7}+2\beta q^{11}-5\beta q^{13}+\cdots\)
1152.4.d.i	$1152$	$4$	1152.d	8.b	$2$	$4$	$4$	$67.970$	\(\Q(i, \sqrt{13})\)	None					384.4.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-32\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(-8+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1152.4.d.j	$1152$	$4$	1152.d	8.b	$2$	$4$	$4$	$67.970$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None					128.4.b.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{2}q^{7}+7\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\)
1152.4.d.k	$1152$	$4$	1152.d	8.b	$2$	$4$	$4$	$67.970$	\(\Q(i, \sqrt{7})\)	None		✓			1152.4.d.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}-10\beta _{1}q^{13}+\cdots\)
1152.4.d.l	$1152$	$4$	1152.d	8.b	$2$	$4$	$4$	$67.970$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		✓			1152.4.d.l	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{11}+17q^{25}+\cdots\)
1152.4.d.m	$1152$	$4$	1152.d	8.b	$2$	$4$	$4$	$67.970$	\(\Q(i, \sqrt{7})\)	None		✓			1152.4.d.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{3}q^{11}+10\beta _{1}q^{13}+\cdots\)
1152.4.d.n	$1152$	$4$	1152.d	8.b	$2$	$4$	$4$	$67.970$	\(\Q(\zeta_{8})\)	None					384.4.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}+5\beta_{3} q^{7}-5\beta_1 q^{11}+14\beta_{2} q^{13}+\cdots\)
1152.4.d.o	$1152$	$4$	1152.d	8.b	$2$	$4$	$4$	$67.970$	\(\Q(i, \sqrt{13})\)	None					384.4.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(32\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(8-\beta _{3})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1152.4.d.p	$1152$	$4$	1152.d	8.b	$2$	$8$	$8$	$67.970$	8.0.1534132224.8	None					384.4.d.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots\)
1152.4.d.q	$1152$	$4$	1152.d	8.b	$2$	$8$	$8$	$67.970$	8.0.\(\cdots\).260	None		✓			1152.4.d.q	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{6}q^{11}-\beta _{3}q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

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