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

\( 928 q - 20 q^{4} - 6 q^{6} - 32 q^{7} - 20 q^{9} + O(q^{10}) \)

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	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	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(-4\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(-1+\beta _{4}+\beta _{6}-\beta _{8}+\beta _{12})q^{2}+\cdots\)
600.2.bp.b	$600$	$2$	600.bp	600.ap	$20$	$16$	$2$	$4.791$	16.0.\(\cdots\).9	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(4\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(1-\beta _{4}-\beta _{6}+\beta _{8}-\beta _{12})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
600.2.bp.c	$600$	$2$	600.bp	600.ap	$20$	$896$	$112$	$4.791$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)		$\mathrm{SU}(2)[C_{20}]$