Space of modular forms of level 208, weight 2, and Character 208.bj

• Label: 208.2.bj
• Level: $208$
• Weight: $2$
• Character orbit: 208.bj
• Rep. character: $\chi_{208}(29,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $104$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.bj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(208, [\chi])\).

	Total	New	Old
Modular forms	120	120	0
Cusp forms	104	104	0
Eisenstein series	16	16	0

Trace form

\( 104 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(208, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
208.2.bj.a	$208$	$2$	208.bj	208.aj	$12$	$104$	$26$	$1.661$		None		✓	✓	✓	208.2.bj.a	$4$	$0$	\(-2\)	\(-2\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$