Space of modular forms of level 440, weight 2, and Character 440.g

• Label: 440.2.g
• Level: $440$
• Weight: $2$
• Character orbit: 440.g
• Rep. character: $\chi_{440}(221,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$440 = 2^{3} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	440.g (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$8$
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$144$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(440, [\chi])$.

	Total	New	Old
Modular forms	76	40	36
Cusp forms	68	40	28
Eisenstein series	8	0	8

Trace form

40 * q + 4 * q^4 - 8 * q^6 + 12 * q^8 - 40 * q^9 - 4 * q^10 + 8 * q^12 + 16 * q^14 - 8 * q^15 - 8 * q^18 - 4 * q^20 + 24 * q^23 - 24 * q^24 - 40 * q^25 + 36 * q^26 - 20 * q^28 + 16 * q^31 + 16 * q^34 - 8 * q^36 - 48 * q^39 + 16 * q^40 - 40 * q^42 - 4 * q^44 - 32 * q^46 - 40 * q^47 - 8 * q^48 + 72 * q^49 + 36 * q^52 + 40 * q^54 + 8 * q^55 - 24 * q^56 - 32 * q^57 - 64 * q^58 + 4 * q^60 - 8 * q^62 + 80 * q^63 + 4 * q^64 - 20 * q^66 + 4 * q^68 - 4 * q^70 - 16 * q^71 - 92 * q^72 - 32 * q^73 - 16 * q^74 + 64 * q^78 - 16 * q^79 + 16 * q^80 + 56 * q^81 + 8 * q^82 + 112 * q^84 + 44 * q^86 + 48 * q^87 - 16 * q^89 - 20 * q^90 + 88 * q^92 + 56 * q^94 - 88 * q^96 + 32 * q^97 - 112 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(440, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
440.2.g.a	$440$	$2$	440.g	8.b	$2$	$4$	$4$	$3.513$	$\Q(\zeta_{8})$	None		✓			440.2.g.a	$2$	$0$	$0$	$0$	$0$	$-4$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{3} q^{2}+(\beta_{2}-\beta_1)q^{3}+2 q^{4}+\cdots$
440.2.g.b	$440$	$2$	440.g	8.b	$2$	$12$	$12$	$3.513$	12.0.$\cdots$.1	None		✓			440.2.g.b	$2$	$0$	$0$	$0$	$0$	$4$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{5}q^{4}-\beta _{8}q^{5}+\cdots$
440.2.g.c	$440$	$2$	440.g	8.b	$2$	$24$	$24$	$3.513$		None		✓	✓		440.2.g.c	$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{2}^{\mathrm{old}}(440, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(440, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(40, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(88, [\chi])$$^{\oplus 2}$