Space of modular forms of level 544, weight 2, and Character 544.b

• Label: 544.2.b
• Level: $544$
• Weight: $2$
• Character orbit: 544.b
• Rep. character: $\chi_{544}(33,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $5$
• Sturm bound: $144$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(544, [\chi])\).

	Total	New	Old
Modular forms	80	18	62
Cusp forms	64	18	46
Eisenstein series	16	0	16

Trace form

\( 18 q - 26 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(544, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
544.2.b.a	$544$	$2$	544.b	17.b	$2$	$2$	$2$	$4.344$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}+3q^{9}-6q^{13}+(1+i)q^{17}+\cdots\)
544.2.b.b	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2312.1	\(\Q(\sqrt{-17}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(-4-\beta _{3})q^{9}+\cdots\)
544.2.b.c	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2312.1	\(\Q(\sqrt{-17}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
544.2.b.d	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots\)
544.2.b.e	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(544, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(544, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 5}\)