Space of modular forms of level 560, weight 4, and Character 560.q

• Label: 560.4.q
• Level: $560$
• Weight: $4$
• Character orbit: 560.q
• Rep. character: $\chi_{560}(81,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $18$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$560 = 2^{4} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	560.q (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$7$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$18$
Sturm bound:			$384$
Trace bound:			$7$
Distinguishing $T_p$:			$3$, $11$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(560, [\chi])$.

	Total	New	Old
Modular forms	600	96	504
Cusp forms	552	96	456
Eisenstein series	48	0	48

Trace form

96 * q + 12 * q^3 - 36 * q^7 - 432 * q^9 + 20 * q^11 + 180 * q^19 - 68 * q^21 + 164 * q^23 - 1200 * q^25 - 864 * q^27 - 344 * q^29 - 240 * q^31 + 8 * q^37 + 696 * q^39 - 296 * q^41 - 1480 * q^43 - 220 * q^45 - 940 * q^47 + 464 * q^49 + 544 * q^51 + 16 * q^53 + 880 * q^55 + 336 * q^57 + 344 * q^59 + 200 * q^61 - 1336 * q^63 - 140 * q^65 - 264 * q^67 - 4112 * q^69 + 160 * q^71 + 216 * q^73 + 300 * q^75 + 1496 * q^77 - 552 * q^79 - 4196 * q^81 - 3536 * q^83 - 4644 * q^87 + 644 * q^89 - 4232 * q^91 - 112 * q^93 + 3168 * q^97 + 4488 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(560, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.4.q.a	$560$	$4$	560.q	7.c	$3$	$2$	$1$	$33.041$	$\Q(\sqrt{-3})$	None					140.4.i.a	$2$	$0$	$0$	$-2$	$-5$	$-20$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{5}+(-1-18\zeta_{6})q^{7}+\cdots$
560.4.q.b	$560$	$4$	560.q	7.c	$3$	$2$	$1$	$33.041$	$\Q(\sqrt{-3})$	None					35.4.e.a	$2$	$0$	$0$	$-2$	$-5$	$28$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{5}+(7+14\zeta_{6})q^{7}+\cdots$
560.4.q.c	$560$	$4$	560.q	7.c	$3$	$2$	$1$	$33.041$	$\Q(\sqrt{-3})$	None					140.4.i.b	$2$	$0$	$0$	$-2$	$5$	$28$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+5\zeta_{6}q^{5}+(21-14\zeta_{6})q^{7}+\cdots$
560.4.q.d	$560$	$4$	560.q	7.c	$3$	$2$	$1$	$33.041$	$\Q(\sqrt{-3})$	None					70.4.e.c	$2$	$0$	$0$	$-1$	$5$	$-17$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+5\zeta_{6}q^{5}+(1-19\zeta_{6})q^{7}+\cdots$
560.4.q.e	$560$	$4$	560.q	7.c	$3$	$2$	$1$	$33.041$	$\Q(\sqrt{-3})$	None					70.4.e.a	$2$	$0$	$0$	$1$	$5$	$-35$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+5\zeta_{6}q^{5}+(-21+7\zeta_{6})q^{7}+\cdots$
560.4.q.f	$560$	$4$	560.q	7.c	$3$	$2$	$1$	$33.041$	$\Q(\sqrt{-3})$	None					280.4.q.a	$2$	$0$	$0$	$7$	$5$	$-7$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(7-7\zeta_{6})q^{3}+5\zeta_{6}q^{5}+(7-21\zeta_{6})q^{7}+\cdots$
560.4.q.g	$560$	$4$	560.q	7.c	$3$	$2$	$1$	$33.041$	$\Q(\sqrt{-3})$	None					70.4.e.b	$2$	$0$	$0$	$10$	$5$	$-28$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(10-10\zeta_{6})q^{3}+5\zeta_{6}q^{5}+(-21+\cdots)q^{7}+\cdots$
560.4.q.h	$560$	$4$	560.q	7.c	$3$	$4$	$2$	$33.041$	$\Q(\sqrt{-3}, \sqrt{46})$	None					140.4.i.e	$2$	$0$	$0$	$-6$	$-10$	$6$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+\beta _{1}-3\beta _{2})q^{3}+5\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
560.4.q.i	$560$	$4$	560.q	7.c	$3$	$4$	$2$	$33.041$	$\Q(\sqrt{2}, \sqrt{-3})$	None					35.4.e.b	$2$	$0$	$0$	$-2$	$-10$	$-22$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3\beta _{1}+\beta _{2}+3\beta _{3})q^{3}+(-5-5\beta _{2}+\cdots)q^{5}+\cdots$
560.4.q.j	$560$	$4$	560.q	7.c	$3$	$4$	$2$	$33.041$	$\Q(\sqrt{-3}, \sqrt{46})$	None					70.4.e.d	$2$	$0$	$0$	$-2$	$-10$	$-6$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+5\beta _{2}q^{5}+(1+\cdots)q^{7}+\cdots$
560.4.q.k	$560$	$4$	560.q	7.c	$3$	$4$	$2$	$33.041$	$\Q(\sqrt{-3}, \sqrt{37})$	None					140.4.i.d	$2$	$0$	$0$	$0$	$10$	$-36$	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{3}+(5-5\beta _{1})q^{5}+(-8-2\beta _{1}+\cdots)q^{7}+\cdots$
560.4.q.l	$560$	$4$	560.q	7.c	$3$	$4$	$2$	$33.041$	$\Q(\sqrt{-3}, \sqrt{22})$	None					140.4.i.c	$2$	$0$	$0$	$10$	$-10$	$54$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(5+\beta _{1}+5\beta _{2})q^{3}+5\beta _{2}q^{5}+(15+\cdots)q^{7}+\cdots$
560.4.q.m	$560$	$4$	560.q	7.c	$3$	$6$	$3$	$33.041$	6.0.$\cdots$.2	None					70.4.e.e	$2$	$0$	$0$	$4$	$-15$	$-14$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(-5+5\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
560.4.q.n	$560$	$4$	560.q	7.c	$3$	$10$	$5$	$33.041$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None					35.4.e.c	$2$	$0$	$0$	$-8$	$25$	$62$	$2^{8}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}+\beta _{4}-2\beta _{5})q^{3}+(5-5\beta _{5})q^{5}+\cdots$
560.4.q.o	$560$	$4$	560.q	7.c	$3$	$10$	$5$	$33.041$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None					280.4.q.b	$2$	$0$	$0$	$6$	$-25$	$-28$	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{3}-\beta _{7})q^{3}-5\beta _{3}q^{5}+(-3+\cdots)q^{7}+\cdots$
560.4.q.p	$560$	$4$	560.q	7.c	$3$	$12$	$6$	$33.041$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					280.4.q.e	$2$	$0$	$0$	$-8$	$30$	$14$	$2^{10}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}+\beta _{3})q^{3}+5\beta _{3}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
560.4.q.q	$560$	$4$	560.q	7.c	$3$	$12$	$6$	$33.041$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					280.4.q.d	$2$	$0$	$0$	$0$	$-30$	$-16$	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{3}+(-5+5\beta _{2})q^{5}+(-3+4\beta _{2}+\cdots)q^{7}+\cdots$
560.4.q.r	$560$	$4$	560.q	7.c	$3$	$12$	$6$	$33.041$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					280.4.q.c	$2$	$0$	$0$	$7$	$30$	$1$	$2^{14}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{3}+\beta _{5})q^{3}+5\beta _{3}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$

Decomposition of $S_{4}^{\mathrm{old}}(560, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(560, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(7, [\chi])$$^{\oplus 10}$$\oplus$$S_{4}^{\mathrm{new}}(14, [\chi])$$^{\oplus 8}$$\oplus$$S_{4}^{\mathrm{new}}(28, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(35, [\chi])$$^{\oplus 5}$$\oplus$$S_{4}^{\mathrm{new}}(56, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(70, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(112, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(140, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(280, [\chi])$$^{\oplus 2}$