Space of modular forms of level 16, weight 2, and Character 16.e

• Label: 16.2.e
• Level: $16$
• Weight: $2$
• Character orbit: 16.e
• Rep. character: $\chi_{16}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(16, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

Trace form

2 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 + 4 * q^6 + 4 * q^8 + 2 * q^11 - 4 * q^12 - 2 * q^13 - 4 * q^14 + 4 * q^15 - 8 * q^16 - 4 * q^17 + 2 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^26 - 8 * q^27 + 8 * q^28 + 6 * q^29 - 4 * q^30 - 16 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 + 6 * q^37 - 12 * q^38 - 8 * q^40 + 10 * q^43 - 4 * q^44 + 2 * q^45 + 12 * q^46 + 16 * q^47 + 8 * q^48 + 6 * q^49 - 6 * q^50 + 4 * q^51 - 4 * q^52 - 10 * q^53 - 8 * q^56 - 12 * q^58 - 6 * q^59 - 18 * q^61 + 16 * q^62 + 4 * q^63 + 4 * q^65 + 4 * q^66 - 10 * q^67 - 12 * q^69 + 8 * q^70 + 4 * q^72 + 6 * q^75 + 12 * q^76 + 4 * q^77 - 4 * q^78 + 8 * q^80 + 10 * q^81 - 2 * q^83 - 8 * q^84 + 4 * q^85 + 8 * q^88 - 4 * q^90 + 4 * q^91 - 24 * q^92 + 16 * q^93 - 16 * q^94 - 12 * q^95 - 16 * q^96 - 4 * q^97 - 6 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(16, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.2.e.a	$16$	$2$	16.e	16.e	$4$	$2$	$1$	$0.128$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	16.2.e.a	$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(i-1)q^{3}+2 i q^{4}+\cdots\)