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

• Label: 600.2.bc
• Level: $600$
• Weight: $2$
• Character orbit: 600.bc
• Rep. character: $\chi_{600}(169,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bc (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	512	56	456
Cusp forms	448	56	392
Eisenstein series	64	0	64

Trace form

56 * q - 4 * q^5 + 14 * q^9 - 2 * q^15 + 12 * q^19 + 4 * q^21 + 60 * q^23 - 6 * q^25 + 16 * q^29 - 6 * q^31 - 4 * q^35 + 20 * q^37 - 16 * q^41 + 4 * q^45 + 40 * q^47 - 12 * q^49 + 48 * q^51 + 60 * q^53 + 32 * q^55 + 24 * q^59 - 4 * q^61 + 16 * q^65 - 8 * q^69 - 24 * q^71 - 40 * q^73 - 8 * q^75 - 4 * q^79 - 14 * q^81 - 60 * q^83 - 48 * q^85 - 60 * q^87 - 24 * q^89 - 8 * q^91 - 88 * q^95 - 30 * 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.bc.a	$600$	$2$	600.bc	25.e	$10$	$8$	$2$	$4.791$	\(\Q(\zeta_{20})\)	None		✓			600.2.bc.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\zeta_{20}q^{3}+(\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{5}+\cdots\)
600.2.bc.b	$600$	$2$	600.bc	25.e	$10$	$24$	$6$	$4.791$		None		✓			600.2.bc.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
600.2.bc.c	$600$	$2$	600.bc	25.e	$10$	$24$	$6$	$4.791$		None		✓			600.2.bc.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)