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

• Label: 600.2.bu
• Level: $600$
• Weight: $2$
• Character orbit: 600.bu
• Rep. character: $\chi_{600}(17,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $240$
• 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.bu (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
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	1024	240	784
Cusp forms	896	240	656
Eisenstein series	128	0	128

Trace form

240 * q - 4 * q^7 - 8 * q^13 + 12 * q^15 + 8 * q^25 + 24 * q^27 + 12 * q^33 + 32 * q^37 + 40 * q^39 + 64 * q^45 - 28 * q^55 + 40 * q^57 - 4 * q^63 - 40 * q^67 - 20 * q^73 - 72 * q^85 + 20 * q^87 + 24 * q^93 - 16 * q^97

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.bu.a	$600$	$2$	600.bu	75.l	$20$	$240$	$30$	$4.791$		None		✓	✓	✓	600.2.bu.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{20}]$

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

\( S_{2}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)