Space of modular forms of level 300, weight 2, and Character 300.w

• Label: 300.2.w
• Level: $300$
• Weight: $2$
• Character orbit: 300.w
• Rep. character: $\chi_{300}(67,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$300 = 2^{2} \cdot 3 \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	300.w (of order $20$ and degree $8$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$100$
Character field:			$\Q(\zeta_{20})$
Newform subspaces:			$1$
Sturm bound:			$120$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(300, [\chi])$.

	Total	New	Old
Modular forms	512	240	272
Cusp forms	448	240	208
Eisenstein series	64	0	64

Trace form

240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(300, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.2.w.a	$300$	$2$	300.w	100.l	$20$	$240$	$30$	$2.396$		None		✓	✓	✓	300.2.w.a	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{20}]$

Decomposition of $S_{2}^{\mathrm{old}}(300, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(300, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(100, [\chi])$$^{\oplus 2}$