Space of modular forms of level 16, weight 8, and Character 16.e

• Label: 16.8.e
• Level: $16$
• Weight: $8$
• Character orbit: 16.e
• Rep. character: $\chi_{16}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $26$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(16, [\chi])\).

	Total	New	Old
Modular forms	30	30	0
Cusp forms	26	26	0
Eisenstein series	4	4	0

Trace form

26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(16, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.8.e.a	$16$	$8$	16.e	16.e	$4$	$26$	$13$	$4.998$		None		✓	✓	✓	16.8.e.a	$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$