Space of modular forms of level 567, weight 4, and Character 567.c

• Label: 567.4.c
• Level: $567$
• Weight: $4$
• Character orbit: 567.c
• Rep. character: $\chi_{567}(566,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	567.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(567, [\chi])\).

	Total	New	Old
Modular forms	228	100	128
Cusp forms	204	92	112
Eisenstein series	24	8	16

Trace form

\( 92 q - 348 q^{4} + 14 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(567, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
567.4.c.a	$567$	$4$	567.c	21.c	$2$	$8$	$8$	$33.454$	8.0.\(\cdots\).3	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{9}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+(-8+3\beta _{1}-\beta _{3})q^{4}-7\beta _{1}q^{7}+\cdots\)
567.4.c.b	$567$	$4$	567.c	21.c	$2$	$40$	$40$	$33.454$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)		$\mathrm{SU}(2)[C_{2}]$
567.4.c.c	$567$	$4$	567.c	21.c	$2$	$44$	$44$	$33.454$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)