Space of modular forms of level 800, weight 2, and Character 800.ba

• Label: 800.2.ba
• Level: $800$
• Weight: $2$
• Character orbit: 800.ba
• Rep. character: $\chi_{800}(149,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $280$
• Newform subspaces: $8$
• Sturm bound: $240$
• Trace bound: $16$

Defining parameters

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.ba (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 160 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(240\)
Trace bound:			\(16\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).

	Total	New	Old
Modular forms	504	296	208
Cusp forms	456	280	176
Eisenstein series	48	16	32

Trace form

\( 280 q + 8 q^{4} - 8 q^{6} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(800, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
800.2.ba.a	$800$	$2$	800.ba	160.z	$8$	$4$	$1$	$6.388$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{3})q^{3}+\cdots\)
800.2.ba.b	$800$	$2$	800.ba	160.z	$8$	$4$	$1$	$6.388$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+(1-\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\)
800.2.ba.c	$800$	$2$	800.ba	160.z	$8$	$8$	$2$	$6.388$	8.0.18939904.2	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\beta _{3}-\beta _{7})q^{2}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
800.2.ba.d	$800$	$2$	800.ba	160.z	$8$	$8$	$2$	$6.388$	8.0.18939904.2	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{3}-\beta _{5}+\beta _{7})q^{3}+\cdots\)
800.2.ba.e	$800$	$2$	800.ba	160.z	$8$	$64$	$16$	$6.388$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
800.2.ba.f	$800$	$2$	800.ba	160.z	$8$	$64$	$16$	$6.388$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
800.2.ba.g	$800$	$2$	800.ba	160.z	$8$	$64$	$16$	$6.388$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
800.2.ba.h	$800$	$2$	800.ba	160.z	$8$	$64$	$16$	$6.388$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)