Space of modular forms of level 26, weight 8, and Character 26.e

• Label: 26.8.e
• Level: $26$
• Weight: $8$
• Character orbit: 26.e
• Rep. character: $\chi_{26}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$26 = 2 \cdot 13$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	26.e (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$13$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$1$
Sturm bound:			$28$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{8}(26, [\chi])$.

	Total	New	Old
Modular forms	52	16	36
Cusp forms	44	16	28
Eisenstein series	8	0	8

Trace form

16 * q + 512 * q^4 + 2520 * q^7 - 4684 * q^9 + 2432 * q^10 - 8496 * q^11 - 3620 * q^13 + 34560 * q^14 + 51648 * q^15 - 32768 * q^16 + 41520 * q^17 - 54432 * q^19 - 16128 * q^20 - 17280 * q^22 - 7560 * q^23 - 273960 * q^25 + 51072 * q^26 + 133920 * q^27 + 161280 * q^28 - 346056 * q^29 + 170368 * q^30 + 486300 * q^33 - 283248 * q^35 + 299776 * q^36 - 68280 * q^37 - 1059840 * q^38 - 1122680 * q^39 + 311296 * q^40 - 1288008 * q^41 + 408320 * q^42 + 285360 * q^43 + 5743980 * q^45 - 188928 * q^46 - 2131660 * q^49 + 85248 * q^50 + 957280 * q^51 + 354560 * q^52 + 3666600 * q^53 - 4074624 * q^54 - 1091472 * q^55 + 1105920 * q^56 + 3504000 * q^58 + 1799280 * q^59 - 4626000 * q^61 - 2770560 * q^62 - 8609760 * q^63 - 4194304 * q^64 - 11518020 * q^65 + 7941120 * q^66 - 7094400 * q^67 - 2657280 * q^68 + 18027316 * q^69 + 25958520 * q^71 + 4423680 * q^72 - 1142400 * q^74 - 10898032 * q^75 - 3483648 * q^76 - 20577480 * q^77 - 22023040 * q^78 + 34143488 * q^79 - 1032192 * q^80 - 15745864 * q^81 + 12202240 * q^82 + 17311488 * q^84 + 7123932 * q^85 - 10460440 * q^87 + 1105920 * q^88 + 10609452 * q^89 + 4070656 * q^90 - 38683952 * q^91 - 967680 * q^92 - 52747080 * q^93 - 14303616 * q^94 + 33837504 * q^95 + 83706300 * q^97 + 19031040 * q^98

Decomposition of $S_{8}^{\mathrm{new}}(26, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
26.8.e.a	$26$	$8$	26.e	13.e	$6$	$16$	$8$	$8.122$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	26.8.e.a	$2$	$0$	$0$	$0$	$0$	$2520$	$2^{34}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{7}-\beta _{9})q^{2}+\beta _{3}q^{3}+2^{6}\beta _{1}q^{4}+\cdots$

Decomposition of $S_{8}^{\mathrm{old}}(26, [\chi])$ into lower level spaces

$S_{8}^{\mathrm{old}}(26, [\chi]) \simeq$ $S_{8}^{\mathrm{new}}(13, [\chi])$$^{\oplus 2}$