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

• Label: 600.2.be
• Level: $600$
• Weight: $2$
• Character orbit: 600.be
• Rep. character: $\chi_{600}(109,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $240$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.be (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	496	240	256
Cusp forms	464	240	224
Eisenstein series	32	0	32

Trace form

240 * q - 30 * q^8 - 60 * q^9 + 10 * q^10 + 12 * q^14 + 12 * q^16 + 4 * q^20 + 50 * q^22 - 4 * q^25 + 20 * q^26 + 28 * q^30 + 24 * q^31 - 16 * q^34 - 30 * q^38 + 16 * q^39 + 28 * q^40 + 8 * q^41 + 42 * q^44 - 20 * q^46 - 240 * q^49 - 20 * q^50 + 140 * q^52 + 16 * q^55 - 36 * q^56 - 10 * q^58 + 22 * q^60 - 50 * q^62 + 42 * q^64 - 76 * q^65 - 8 * q^66 - 32 * q^70 + 30 * q^72 - 44 * q^74 - 8 * q^76 - 40 * q^79 + 12 * q^80 - 60 * q^81 - 24 * q^84 + 60 * q^86 - 170 * q^88 - 60 * q^89 - 20 * q^90 - 190 * q^92 - 30 * q^94 + 136 * q^95 - 20 * q^96 + 40 * q^97 - 140 * 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.be.a	$600$	$2$	600.be	200.o	$10$	$120$	$30$	$4.791$		None		✓			600.2.be.a	$2$	$0$	\(0\)	\(-30\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
600.2.be.b	$600$	$2$	600.be	200.o	$10$	$120$	$30$	$4.791$		None		✓			600.2.be.a	$2$	$0$	\(0\)	\(30\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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