Space of modular forms of level 51, weight 2, and Character 51.d

• Label: 51.2.d
• Level: $51$
• Weight: $2$
• Character orbit: 51.d
• Rep. character: $\chi_{51}(16,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(51, [\chi])\).

	Total	New	Old
Modular forms	8	4	4
Cusp forms	4	4	0
Eisenstein series	4	0	4

Trace form

\( 4 q - 2 q^{2} + 2 q^{4} - 6 q^{8} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(51, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
51.2.d.a	$51$	$2$	51.d	17.b	$2$	$2$	$2$	$0.407$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+iq^{3}+2q^{4}+3iq^{5}-2iq^{6}+\cdots\)
51.2.d.b	$51$	$2$	51.d	17.b	$2$	$2$	$2$	$0.407$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+iq^{3}-q^{4}+iq^{6}-4iq^{7}+\cdots\)