Space of modular forms of level 580, weight 4, and Character 580.c

• Label: 580.4.c
• Level: $580$
• Weight: $4$
• Character orbit: 580.c
• Rep. character: $\chi_{580}(349,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $2$
• Sturm bound: $360$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$580 = 2^{2} \cdot 5 \cdot 29$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	580.c (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$360$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(580, [\chi])$.

	Total	New	Old
Modular forms	276	42	234
Cusp forms	264	42	222
Eisenstein series	12	0	12

Trace form

42 * q - 16 * q^5 - 314 * q^9 - 72 * q^11 - 160 * q^15 + 288 * q^19 - 264 * q^21 + 40 * q^25 + 174 * q^29 + 216 * q^31 + 536 * q^35 - 1288 * q^39 - 764 * q^41 + 702 * q^45 - 2782 * q^49 + 1952 * q^51 + 1240 * q^55 + 308 * q^59 - 828 * q^61 + 1662 * q^65 + 472 * q^69 + 408 * q^71 - 2556 * q^75 - 1696 * q^79 + 2042 * q^81 - 2572 * q^85 + 3964 * q^89 + 3736 * q^91 + 1032 * q^95 + 5904 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(580, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
580.4.c.a	$580$	$4$	580.c	5.b	$2$	$18$	$18$	$34.221$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓			580.4.c.a	$2$	$0$	$0$	$0$	$-8$	$0$	$2^{9}\cdot 53^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{16}q^{7}+(-4+\beta _{2}+\cdots)q^{9}+\cdots$
580.4.c.b	$580$	$4$	580.c	5.b	$2$	$24$	$24$	$34.221$		None		✓	✓		580.4.c.b	$2$	$0$	$0$	$0$	$-8$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{4}^{\mathrm{old}}(580, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(580, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(10, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(20, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(145, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(290, [\chi])$$^{\oplus 2}$