Space of modular forms of level 4020, weight 2, and Character 4020.g

• Label: 4020.2.g
• Level: $4020$
• Weight: $2$
• Character orbit: 4020.g
• Rep. character: $\chi_{4020}(1609,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $1632$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4020.g (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$1632$
Trace bound:			$1$
Distinguishing $T_p$:			$7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(4020, [\chi])$.

	Total	New	Old
Modular forms	828	64	764
Cusp forms	804	64	740
Eisenstein series	24	0	24

Trace form

64 * q - 4 * q^5 - 64 * q^9 + 16 * q^11 + 4 * q^15 - 8 * q^21 + 8 * q^25 - 32 * q^29 - 8 * q^31 - 4 * q^35 + 24 * q^41 + 4 * q^45 - 56 * q^49 + 8 * q^55 - 32 * q^59 + 24 * q^61 + 4 * q^65 + 8 * q^75 - 24 * q^79 + 64 * q^81 - 8 * q^85 - 24 * q^89 + 24 * q^91 + 32 * q^95 - 16 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(4020, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4020.2.g.a	$4020$	$2$	4020.g	5.b	$2$	$2$	$2$	$32.100$	$\Q(\sqrt{-1})$	None		✓			4020.2.g.a	$2$	$0$	$0$	$0$	$2$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-2 i+1)q^{5}-q^{9}+2 i q^{13}+\cdots$
4020.2.g.b	$4020$	$2$	4020.g	5.b	$2$	$24$	$24$	$32.100$		None		✓			4020.2.g.b	$2$	$0$	$0$	$0$	$-4$	$0$		$\mathrm{SU}(2)[C_{2}]$
4020.2.g.c	$4020$	$2$	4020.g	5.b	$2$	$38$	$38$	$32.100$		None		✓	✓		4020.2.g.c	$2$	$0$	$0$	$0$	$-2$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{2}^{\mathrm{old}}(4020, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(4020, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(30, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(60, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(335, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(670, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1005, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(1340, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(2010, [\chi])$$^{\oplus 2}$