Space of modular forms of level 8, weight 5, and Character 8.d

• Label: 8.5.d
• Level: $8$
• Weight: $5$
• Character orbit: 8.d
• Rep. character: $\chi_{8}(3,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $5$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(5\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(8, [\chi])\).

	Total	New	Old
Modular forms	5	5	0
Cusp forms	3	3	0
Eisenstein series	2	2	0

Trace form

3 * q + 2 * q^2 - 2 * q^3 - 12 * q^4 - 68 * q^6 + 152 * q^8 + 25 * q^9 + 240 * q^10 - 98 * q^11 - 392 * q^12 - 480 * q^14 + 528 * q^16 - 122 * q^17 + 550 * q^18 + 702 * q^19 - 480 * q^20 - 132 * q^22 - 368 * q^24 - 45 * q^25 - 240 * q^26 - 1988 * q^27 + 960 * q^28 + 1440 * q^30 - 928 * q^32 + 332 * q^33 - 2748 * q^34 + 3840 * q^35 + 3100 * q^36 + 1468 * q^38 - 2880 * q^40 + 742 * q^41 - 2880 * q^42 - 7266 * q^43 - 8 * q^44 + 2400 * q^46 - 1952 * q^48 - 477 * q^49 + 3170 * q^50 + 10748 * q^51 + 480 * q^52 - 392 * q^54 + 5760 * q^56 - 4468 * q^57 + 2640 * q^58 - 10274 * q^59 - 2880 * q^60 - 9600 * q^62 + 3648 * q^64 + 1920 * q^65 + 2888 * q^66 + 10878 * q^67 - 15512 * q^68 - 3840 * q^70 + 3400 * q^72 + 10278 * q^73 + 13680 * q^74 - 12770 * q^75 + 3192 * q^76 - 1440 * q^78 + 13440 * q^80 - 4433 * q^81 - 6972 * q^82 + 6718 * q^83 + 5760 * q^84 - 10244 * q^86 - 5232 * q^88 - 14618 * q^89 - 10800 * q^90 - 3840 * q^91 - 4800 * q^92 + 16320 * q^94 - 26048 * q^96 + 7494 * q^97 + 12482 * q^98 - 2950 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(8, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.5.d.a	$8$	$5$	8.d	8.d	$2$	$1$	$1$	$0.827$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	✓			8.5.d.a	$2$	$0$	\(4\)	\(-14\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
8.5.d.b	$8$	$5$	8.d	8.d	$2$	$2$	$2$	$0.827$	\(\Q(\sqrt{-15}) \)	None		✓	✓		8.5.d.b	$2$	$0$	\(-2\)	\(12\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)