Space of modular forms of level 600, weight 3, and Character 600.p

• Label: 600.3.p
• Level: $600$
• Weight: $3$
• Character orbit: 600.p
• Rep. character: $\chi_{600}(499,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $360$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	600.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(360\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(600, [\chi])\).

	Total	New	Old
Modular forms	252	72	180
Cusp forms	228	72	156
Eisenstein series	24	0	24

Trace form

72 * q - 4 * q^4 + 12 * q^6 - 216 * q^9 - 76 * q^14 - 60 * q^16 + 64 * q^19 + 36 * q^24 + 12 * q^26 + 272 * q^34 + 12 * q^36 + 80 * q^41 - 304 * q^44 - 16 * q^46 + 504 * q^49 + 192 * q^51 - 36 * q^54 - 56 * q^56 - 256 * q^59 + 260 * q^64 - 192 * q^66 + 120 * q^74 + 304 * q^76 + 648 * q^81 - 456 * q^84 + 404 * q^86 + 400 * q^89 - 768 * q^91 - 1072 * q^94 - 252 * q^96

Decomposition of \(S_{3}^{\mathrm{new}}(600, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
600.3.p.a	$600$	$3$	600.p	40.e	$2$	$8$	$8$	$16.349$	8.0.22581504.2	None					24.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{4}q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\)
600.3.p.b	$600$	$3$	600.p	40.e	$2$	$32$	$32$	$16.349$		None					120.3.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
600.3.p.c	$600$	$3$	600.p	40.e	$2$	$32$	$32$	$16.349$		None		✓			600.3.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)