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

• Label: 208.2.f
• Level: $208$
• Weight: $2$
• Character orbit: 208.f
• Rep. character: $\chi_{208}(129,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	34	8	26
Cusp forms	22	6	16
Eisenstein series	12	2	10

Trace form

\( 6 q + 4 q^{3} + 2 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
208.2.f.a	$208$	$2$	208.f	13.b	$2$	$2$	$2$	$1.661$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+iq^{5}+iq^{7}-2q^{9}+(2-i)q^{13}+\cdots\)
208.2.f.b	$208$	$2$	208.f	13.b	$2$	$4$	$4$	$1.661$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(208, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(208, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)