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

• Label: 600.2.bp
• Level: $600$
• Weight: $2$
• Character orbit: 600.bp
• Rep. character: $\chi_{600}(53,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $928$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bp (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 600 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	992	992	0
Cusp forms	928	928	0
Eisenstein series	64	64	0

Trace form

928 * q - 20 * q^4 - 6 * q^6 - 32 * q^7 - 20 * q^9 - 8 * q^10 - 2 * q^12 - 16 * q^15 - 12 * q^16 + 10 * q^18 - 32 * q^25 - 48 * q^28 + 22 * q^30 - 24 * q^31 - 4 * q^33 - 20 * q^34 - 22 * q^36 - 20 * q^39 - 44 * q^40 - 78 * q^42 - 12 * q^46 + 76 * q^48 - 28 * q^52 - 140 * q^54 + 8 * q^55 - 4 * q^57 - 64 * q^58 + 34 * q^60 - 44 * q^63 - 20 * q^64 + 18 * q^66 - 104 * q^70 - 42 * q^72 - 32 * q^73 - 104 * q^78 - 40 * q^79 - 12 * q^81 - 124 * q^82 - 10 * q^84 - 84 * q^87 - 24 * q^88 - 94 * q^90 - 300 * q^94 - 6 * q^96 + 32 * 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.bp.a	$600$	$2$	600.bp	600.ap	$20$	$16$	$2$	$4.791$	16.0.\(\cdots\).9	\(\Q(\sqrt{-6}) \)		✓			600.2.bp.a	$4$	$0$	\(-4\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(-1+\beta _{4}+\beta _{6}-\beta _{8}+\beta _{12})q^{2}+\cdots\)
600.2.bp.b	$600$	$2$	600.bp	600.ap	$20$	$16$	$2$	$4.791$	16.0.\(\cdots\).9	\(\Q(\sqrt{-6}) \)		✓			600.2.bp.a	$4$	$0$	\(4\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(1-\beta _{4}-\beta _{6}+\beta _{8}-\beta _{12})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
600.2.bp.c	$600$	$2$	600.bp	600.ap	$20$	$896$	$112$	$4.791$		None		✓	✓		600.2.bp.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)		$\mathrm{SU}(2)[C_{20}]$