Space of modular forms of level 16, weight 5, and Character 16.f

• Label: 16.5.f
• Level: $16$
• Weight: $5$
• Character orbit: 16.f
• Rep. character: $\chi_{16}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(16, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	14	14	0
Eisenstein series	4	4	0

Trace form

14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8 - 100 * q^10 + 94 * q^11 - 332 * q^12 - 2 * q^13 + 44 * q^14 - 168 * q^16 - 4 * q^17 + 1390 * q^18 - 706 * q^19 + 1900 * q^20 - 164 * q^21 + 900 * q^22 + 1148 * q^23 - 1872 * q^24 - 3416 * q^26 - 1664 * q^27 - 3784 * q^28 + 862 * q^29 - 3740 * q^30 + 3208 * q^32 - 4 * q^33 + 7508 * q^34 + 1340 * q^35 + 11468 * q^36 - 1826 * q^37 + 3568 * q^38 + 2684 * q^39 - 5144 * q^40 - 17064 * q^42 + 1694 * q^43 - 14636 * q^44 + 1410 * q^45 - 5316 * q^46 + 6888 * q^48 + 682 * q^49 + 20070 * q^50 - 3012 * q^51 + 20452 * q^52 - 482 * q^53 + 10784 * q^54 - 11780 * q^55 - 6952 * q^56 - 20456 * q^58 - 2786 * q^59 - 29920 * q^60 - 3778 * q^61 - 11472 * q^62 + 15808 * q^64 - 2020 * q^65 + 30148 * q^66 + 7998 * q^67 + 18032 * q^68 + 9628 * q^69 + 15296 * q^70 + 19964 * q^71 - 17708 * q^72 - 23780 * q^74 + 17570 * q^75 - 23996 * q^76 - 9508 * q^77 - 8052 * q^78 + 1384 * q^80 + 1454 * q^81 + 16016 * q^82 - 17282 * q^83 + 19624 * q^84 + 9948 * q^85 - 4796 * q^86 - 49284 * q^87 + 7288 * q^88 - 5416 * q^90 - 28036 * q^91 - 14632 * q^92 + 8896 * q^93 + 432 * q^94 + 6064 * q^96 - 4 * q^97 - 12246 * q^98 + 49214 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(16, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.5.f.a	$16$	$5$	16.f	16.f	$4$	$14$	$7$	$1.654$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓	✓	16.5.f.a	$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)	$2^{21}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots\)