Space of modular forms of level 676, weight 2, and Character 676.d

• Label: 676.2.d
• Level: $676$
• Weight: $2$
• Character orbit: 676.d
• Rep. character: $\chi_{676}(337,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $5$
• Sturm bound: $182$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(182\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(676, [\chi])\).

	Total	New	Old
Modular forms	112	14	98
Cusp forms	70	14	56
Eisenstein series	42	0	42

Trace form

\( 14 q + 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(676, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
676.2.d.a	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+3iq^{5}-4iq^{7}+q^{9}-6iq^{15}+\cdots\)
676.2.d.b	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\zeta_{6}q^{7}-2q^{9}+3\zeta_{6}q^{11}+3q^{17}+\cdots\)
676.2.d.c	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+iq^{7}-3q^{9}+iq^{11}-6q^{17}+\cdots\)
676.2.d.d	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+2iq^{5}-iq^{7}+6q^{9}+5iq^{11}+\cdots\)
676.2.d.e	$676$	$2$	676.d	13.b	$2$	$6$	$6$	$5.398$	6.0.153664.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\beta _{2}-\beta _{4})q^{3}+(-\beta _{1}+3\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(676, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(676, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)