Space of modular forms of level 561, weight 2, and Character 561.h

• Label: 561.2.h
• Level: $561$
• Weight: $2$
• Character orbit: 561.h
• Rep. character: $\chi_{561}(560,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 561 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(561, [\chi])\).

	Total	New	Old
Modular forms	76	76	0
Cusp forms	68	68	0
Eisenstein series	8	8	0

Trace form

\( 68 q + 56 q^{4} - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(561, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
561.2.h.a	$561$	$2$	561.h	561.h	$2$	$4$	$4$	$4.480$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\zeta_{8}q^{3}-q^{4}+(\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
561.2.h.b	$561$	$2$	561.h	561.h	$2$	$4$	$4$	$4.480$	\(\Q(\sqrt{3}, \sqrt{-17})\)	\(\Q(\sqrt{-51}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}-2q^{4}-\beta _{2}q^{5}+3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
561.2.h.c	$561$	$2$	561.h	561.h	$2$	$4$	$4$	$4.480$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
561.2.h.d	$561$	$2$	561.h	561.h	$2$	$56$	$56$	$4.480$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$