Space of modular forms of level 289, weight 2, and Character 289.b

• Label: 289.2.b
• Level: $289$
• Weight: $2$
• Character orbit: 289.b
• Rep. character: $\chi_{289}(288,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $51$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(51\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(289, [\chi])\).

	Total	New	Old
Modular forms	34	30	4
Cusp forms	16	16	0
Eisenstein series	18	14	4

Trace form

\( 16 q + 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(289, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
289.2.b.a	$289$	$2$	289.b	17.b	$2$	$2$	$2$	$2.308$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots\)
289.2.b.b	$289$	$2$	289.b	17.b	$2$	$4$	$4$	$2.308$	4.0.2048.2	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.c	$289$	$2$	289.b	17.b	$2$	$4$	$4$	$2.308$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.b.d	$289$	$2$	289.b	17.b	$2$	$6$	$6$	$2.308$	6.0.419904.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots\)