Space of modular forms of level 578, weight 2, and Character 578.d

• Label: 578.2.d
• Level: $578$
• Weight: $2$
• Character orbit: 578.d
• Rep. character: $\chi_{578}(155,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $92$
• Newform subspaces: $9$
• Sturm bound: $153$
• Trace bound: $18$

Defining parameters

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.d (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(153\)
Trace bound:			\(18\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(578, [\chi])\).

	Total	New	Old
Modular forms	380	92	288
Cusp forms	236	92	144
Eisenstein series	144	0	144

Trace form

\( 92 q + 8 q^{5} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(578, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
578.2.d.a	$578$	$2$	578.d	17.d	$8$	$4$	$1$	$4.615$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{8}^{3}q^{2}+(-1-\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
578.2.d.b	$578$	$2$	578.d	17.d	$8$	$4$	$1$	$4.615$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
578.2.d.c	$578$	$2$	578.d	17.d	$8$	$4$	$1$	$4.615$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+(2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
578.2.d.d	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	\(\Q(\zeta_{16})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}q^{2}+\zeta_{16}^{6}q^{3}+\zeta_{16}^{2}q^{4}-2\zeta_{16}^{3}q^{5}+\cdots\)
578.2.d.e	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	\(\Q(\zeta_{16})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)
578.2.d.f	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	\(\Q(\zeta_{16})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	\(q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{3}q^{5}-\zeta_{16}^{4}q^{8}+\cdots\)
578.2.d.g	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	\(\Q(\zeta_{16})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}q^{2}+\zeta_{16}^{6}q^{3}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{3}q^{5}+\cdots\)
578.2.d.h	$578$	$2$	578.d	17.d	$8$	$24$	$6$	$4.615$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
578.2.d.i	$578$	$2$	578.d	17.d	$8$	$24$	$6$	$4.615$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(578, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(578, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)