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

• Label: 600.2.v
• Level: $600$
• Weight: $2$
• Character orbit: 600.v
• Rep. character: $\chi_{600}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	264	72	192
Cusp forms	216	72	144
Eisenstein series	48	0	48

Trace form

72 * q - 8 * q^6 + 12 * q^8 + 8 * q^12 + 40 * q^16 - 8 * q^17 + 28 * q^22 + 32 * q^26 - 4 * q^28 - 20 * q^32 - 8 * q^36 - 40 * q^38 - 20 * q^42 + 32 * q^43 + 24 * q^46 - 16 * q^48 + 32 * q^51 + 48 * q^52 - 56 * q^56 + 12 * q^58 + 16 * q^62 + 48 * q^66 - 48 * q^67 - 72 * q^68 - 12 * q^72 + 40 * q^73 - 96 * q^76 + 24 * q^78 - 72 * q^81 - 24 * q^82 - 80 * q^83 - 56 * q^86 - 12 * q^88 - 128 * q^91 - 16 * q^92 - 32 * q^96 + 24 * q^97 + 88 * 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.v.a	$600$	$2$	600.v	40.k	$4$	$16$	$8$	$4.791$	16.0.\(\cdots\).7	None		✓			600.2.v.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+\beta _{5}q^{6}+\cdots\)
600.2.v.b	$600$	$2$	600.v	40.k	$4$	$24$	$12$	$4.791$		None					120.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
600.2.v.c	$600$	$2$	600.v	40.k	$4$	$32$	$16$	$4.791$		None		✓	✓		600.2.v.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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