Space of modular forms of level 26, weight 3, and Character 26.d

• Label: 26.3.d
• Level: $26$
• Weight: $3$
• Character orbit: 26.d
• Rep. character: $\chi_{26}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	26.d (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(26, [\chi])\).

	Total	New	Old
Modular forms	18	2	16
Cusp forms	10	2	8
Eisenstein series	8	0	8

Trace form

\( 2 q + 2 q^{2} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(26, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
26.3.d.a	$26$	$3$	26.d	13.d	$4$	$2$	$1$	$0.708$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(26, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)