Space of modular forms of level 208, weight 3, and Character 208.o

• Label: 208.3.o
• Level: $208$
• Weight: $3$
• Character orbit: 208.o
• Rep. character: $\chi_{208}(51,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(208, [\chi])\).

	Total	New	Old
Modular forms	116	116	0
Cusp forms	108	108	0
Eisenstein series	8	8	0

Trace form

108 * q - 4 * q^3 - 4 * q^4 - 4 * q^10 - 88 * q^12 - 2 * q^13 + 28 * q^14 - 4 * q^16 - 8 * q^17 - 36 * q^22 - 8 * q^23 - 4 * q^26 - 64 * q^27 - 4 * q^29 + 52 * q^30 + 96 * q^35 + 192 * q^36 - 144 * q^38 + 188 * q^39 + 216 * q^40 + 120 * q^42 + 60 * q^43 - 92 * q^48 - 596 * q^49 - 40 * q^51 - 108 * q^52 - 4 * q^53 + 248 * q^55 + 372 * q^56 - 4 * q^61 - 464 * q^62 - 256 * q^64 - 20 * q^65 - 184 * q^66 - 232 * q^68 - 40 * q^69 + 424 * q^74 + 124 * q^75 + 192 * q^77 - 72 * q^78 - 692 * q^81 - 96 * q^82 - 8 * q^87 - 616 * q^88 - 956 * q^90 + 384 * q^91 + 268 * q^92 + 100 * q^94

Decomposition of \(S_{3}^{\mathrm{new}}(208, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
208.3.o.a	$208$	$3$	208.o	208.o	$4$	$108$	$54$	$5.668$		None		✓	✓	✓	208.3.o.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$