Space of modular forms of level 40, weight 6, and Character 40.c

• Label: 40.6.c
• Level: $40$
• Weight: $6$
• Character orbit: 40.c
• Rep. character: $\chi_{40}(9,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$40 = 2^{3} \cdot 5$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	40.c (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$1$
Sturm bound:			$36$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(40, [\chi])$.

	Total	New	Old
Modular forms	34	8	26
Cusp forms	26	8	18
Eisenstein series	8	0	8

Trace form

8 * q + 8 * q^5 - 1000 * q^9 - 736 * q^11 - 992 * q^15 + 1376 * q^19 + 1984 * q^21 - 2136 * q^25 + 5872 * q^29 + 4224 * q^31 + 19232 * q^35 - 3008 * q^39 + 23600 * q^41 - 28328 * q^45 - 45000 * q^49 - 124800 * q^51 + 15008 * q^55 + 91680 * q^59 + 123856 * q^61 - 72064 * q^65 - 76736 * q^69 - 125632 * q^71 + 222784 * q^75 + 43264 * q^79 + 409672 * q^81 - 293760 * q^85 - 41904 * q^89 - 487616 * q^91 + 442592 * q^95 + 266848 * q^99

Decomposition of $S_{6}^{\mathrm{new}}(40, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
40.6.c.a	$40$	$6$	40.c	5.b	$2$	$8$	$8$	$6.415$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	40.6.c.a	$2$	$0$	$0$	$0$	$8$	$0$	$2^{31}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(\beta _{2}+\beta _{6})q^{7}+\cdots$

Decomposition of $S_{6}^{\mathrm{old}}(40, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(40, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(5, [\chi])$$^{\oplus 4}$$\oplus$$S_{6}^{\mathrm{new}}(10, [\chi])$$^{\oplus 3}$$\oplus$$S_{6}^{\mathrm{new}}(20, [\chi])$$^{\oplus 2}$