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

• Label: 208.2.bm
• Level: $208$
• Weight: $2$
• Character orbit: 208.bm
• Rep. character: $\chi_{208}(15,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $28$
• Newform subspaces: $6$
• Sturm bound: $56$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.bm (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(56\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	136	28	108
Cusp forms	88	28	60
Eisenstein series	48	0	48

Trace form

\( 28 q - 6 q^{5} + 14 q^{9} + 8 q^{21} - 38 q^{37} - 36 q^{41} - 60 q^{45} - 24 q^{49} - 36 q^{53} + 32 q^{57} - 54 q^{61} + 12 q^{65} - 14 q^{73} - 14 q^{81} - 18 q^{85} + 78 q^{89} + 88 q^{93} + 50 q^{97}+O(q^{100}) \)

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.bm.a	$208$	$2$	208.bm	52.l	$12$	$4$	$1$	$1.661$	\(\Q(\zeta_{12})\)	None		✓			208.2.bm.a	$2$	$1$	\(0\)	\(-6\)	\(-6\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
208.2.bm.b	$208$	$2$	208.bm	52.l	$12$	$4$	$1$	$1.661$	\(\Q(\zeta_{12})\)	None		✓			208.2.bm.b	$2$	$0$	\(0\)	\(-6\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2+\zeta_{12}^{2})q^{3}+(1-\zeta_{12}^{3})q^{5}+\cdots\)
208.2.bm.c	$208$	$2$	208.bm	52.l	$12$	$4$	$1$	$1.661$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			208.2.bm.c	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-2-3\zeta_{12}+3\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots\)
208.2.bm.d	$208$	$2$	208.bm	52.l	$12$	$4$	$1$	$1.661$	\(\Q(\zeta_{12})\)	None		✓			208.2.bm.a	$2$	$0$	\(0\)	\(6\)	\(-6\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2+\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
208.2.bm.e	$208$	$2$	208.bm	52.l	$12$	$4$	$1$	$1.661$	\(\Q(\zeta_{12})\)	None		✓			208.2.bm.b	$2$	$0$	\(0\)	\(6\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2-\zeta_{12}^{2})q^{3}+(1-\zeta_{12}^{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
208.2.bm.f	$208$	$2$	208.bm	52.l	$12$	$8$	$2$	$1.661$	8.0.454201344.7	None		✓	✓		208.2.bm.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{1}q^{3}+(1-\beta _{2}+\beta _{3}+2\beta _{4})q^{5}+\cdots\)

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

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