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

• Label: 208.4.bm
• Level: $208$
• Weight: $4$
• Character orbit: 208.bm
• Rep. character: $\chi_{208}(15,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $84$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.bm (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	360	84	276
Cusp forms	312	84	228
Eisenstein series	48	0	48

Trace form

\( 84 q + 6 q^{5} + 378 q^{9} + O(q^{10}) \)

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.bm.a	$208$	$4$	208.bm	52.l	$12$	$4$	$1$	$12.272$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-26\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-2+9\zeta_{12}-9\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots\)
208.4.bm.b	$208$	$4$	208.bm	52.l	$12$	$24$	$6$	$12.272$		None		$4$	$0$	\(0\)	\(0\)	\(28\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
208.4.bm.c	$208$	$4$	208.bm	52.l	$12$	$28$	$7$	$12.272$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-48\)		$\mathrm{SU}(2)[C_{12}]$
208.4.bm.d	$208$	$4$	208.bm	52.l	$12$	$28$	$7$	$12.272$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(48\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{4}^{\mathrm{old}}(208, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(208, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)