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

• Label: 578.2.c
• Level: $578$
• Weight: $2$
• Character orbit: 578.c
• Rep. character: $\chi_{578}(251,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $44$
• Newform subspaces: $8$
• Sturm bound: $153$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(153\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	188	44	144
Cusp forms	116	44	72
Eisenstein series	72	0	72

Trace form

\( 44 q + 2 q^{3} - 44 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} + O(q^{10}) \)

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.c.a	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}+(-2-2i)q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
578.2.c.b	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}-3iq^{9}+\cdots\)
578.2.c.c	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}+(1+i)q^{3}-q^{4}+(-2-2i)q^{5}+\cdots\)
578.2.c.d	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}+(2+2i)q^{3}-q^{4}+(2+2i)q^{5}+\cdots\)
578.2.c.e	$578$	$2$	578.c	17.c	$4$	$4$	$2$	$4.615$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{3}q^{6}+\cdots\)
578.2.c.f	$578$	$2$	578.c	17.c	$4$	$8$	$4$	$4.615$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}^{2}q^{2}+\zeta_{16}^{7}q^{3}-q^{4}-2\zeta_{16}^{7}q^{5}+\cdots\)
578.2.c.g	$578$	$2$	578.c	17.c	$4$	$12$	$6$	$4.615$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}+(-\beta _{1}+\beta _{3}+2\beta _{5})q^{3}-q^{4}+\cdots\)
578.2.c.h	$578$	$2$	578.c	17.c	$4$	$12$	$6$	$4.615$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}+(-\beta _{8}+\beta _{10})q^{3}-q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots\)

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

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