Space of modular forms of level 600, weight 2, and Character 600.bq

• Label: 600.2.bq
• Level: $600$
• Weight: $2$
• Character orbit: 600.bq
• Rep. character: $\chi_{600}(67,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $480$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bq (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).

	Total	New	Old
Modular forms	992	480	512
Cusp forms	928	480	448
Eisenstein series	64	0	64

Trace form

480 * q + 12 * q^8 - 8 * q^10 + 8 * q^12 - 8 * q^17 + 20 * q^20 + 28 * q^22 + 8 * q^25 - 4 * q^28 - 8 * q^30 - 20 * q^32 + 48 * q^35 + 20 * q^38 - 108 * q^40 - 20 * q^42 + 32 * q^43 - 140 * q^44 - 16 * q^48 + 124 * q^50 - 132 * q^52 + 152 * q^58 - 20 * q^60 + 116 * q^62 - 60 * q^64 + 8 * q^65 - 48 * q^67 - 72 * q^68 - 4 * q^70 - 12 * q^72 + 40 * q^73 + 24 * q^78 - 76 * q^80 + 120 * q^81 - 64 * q^82 - 80 * q^83 - 80 * q^84 - 132 * q^88 + 200 * q^89 - 48 * q^90 - 216 * q^92 - 40 * q^94 + 20 * q^96 - 56 * q^97 - 192 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(600, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
600.2.bq.a	$600$	$2$	600.bq	200.v	$20$	$480$	$60$	$4.791$		None		✓	✓	✓	600.2.bq.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)