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

• Label: 208.2.n
• Level: $208$
• Weight: $2$
• Character orbit: 208.n
• Rep. character: $\chi_{208}(53,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• 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.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
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	60	48	12
Cusp forms	52	48	4
Eisenstein series	8	0	8

Trace form

48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

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.n.a	$208$	$2$	208.n	16.e	$4$	$48$	$24$	$1.661$		None		✓	✓	✓	208.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(208, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)