Space of modular forms of level 208, weight 4, and Character 208.l

• Label: 208.4.l
• Level: $208$
• Weight: $4$
• Character orbit: 208.l
• Rep. character: $\chi_{208}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $164$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(208, [\chi])\).

	Total	New	Old
Modular forms	172	172	0
Cusp forms	164	164	0
Eisenstein series	8	8	0

Trace form

\( 164 q - 2 q^{2} - 4 q^{3} + 44 q^{6} - 4 q^{7} - 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(208, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
208.4.l.a	$208$	$4$	208.l	208.l	$4$	$164$	$82$	$12.272$		None		$2$	$0$	\(-2\)	\(-4\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$