Space of modular forms of level 833, weight 2, and Character 833.l

• Label: 833.2.l
• Level: $833$
• Weight: $2$
• Character orbit: 833.l
• Rep. character: $\chi_{833}(246,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $228$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $6$

Defining parameters

Level:	$N$	$=$	$833 = 7^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	833.l (of order $8$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$17$
Character field:			$\Q(\zeta_{8})$
Newform subspaces:			$7$
Sturm bound:			$168$
Trace bound:			$6$
Distinguishing $T_p$:			$2$, $3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(833, [\chi])$.

	Total	New	Old
Modular forms	368	268	100
Cusp forms	304	228	76
Eisenstein series	64	40	24

Trace form

228 * q + 4 * q^2 + 4 * q^3 + 12 * q^6 - 28 * q^8 + 16 * q^9 + 12 * q^10 + 12 * q^11 - 20 * q^12 - 16 * q^15 - 172 * q^16 - 8 * q^17 + 36 * q^18 + 16 * q^19 - 20 * q^20 - 36 * q^22 - 12 * q^23 - 52 * q^24 + 12 * q^25 + 20 * q^26 - 32 * q^27 - 20 * q^29 - 4 * q^31 - 92 * q^32 + 16 * q^33 - 12 * q^34 - 32 * q^36 + 8 * q^37 + 32 * q^40 + 12 * q^41 - 56 * q^43 + 148 * q^44 - 4 * q^45 + 28 * q^46 + 92 * q^48 - 124 * q^50 - 28 * q^51 - 80 * q^52 + 84 * q^53 + 16 * q^54 - 40 * q^57 + 8 * q^58 - 8 * q^59 - 32 * q^60 + 48 * q^61 + 100 * q^62 - 52 * q^65 + 32 * q^66 + 16 * q^67 + 36 * q^68 + 16 * q^69 - 76 * q^71 + 20 * q^73 - 132 * q^74 + 36 * q^75 + 24 * q^76 + 24 * q^78 - 60 * q^79 - 56 * q^80 - 44 * q^82 - 48 * q^83 + 28 * q^85 + 40 * q^86 + 24 * q^87 - 4 * q^88 - 20 * q^90 + 116 * q^92 - 56 * q^93 + 128 * q^94 - 40 * q^95 - 92 * q^96 - 16 * q^97 - 164 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(833, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
833.2.l.a	$833$	$2$	833.l	17.d	$8$	$4$	$1$	$6.652$	$\Q(\zeta_{8})$	None					17.2.d.a	$2$	$0$	$-4$	$4$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
833.2.l.b	$833$	$2$	833.l	17.d	$8$	$32$	$8$	$6.652$		None		✓			833.2.l.b	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$
833.2.l.c	$833$	$2$	833.l	17.d	$8$	$32$	$8$	$6.652$		None					119.2.k.a	$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$
833.2.l.d	$833$	$2$	833.l	17.d	$8$	$40$	$10$	$6.652$		None		✓			833.2.l.d	$2$	$0$	$0$	$-4$	$-8$	$0$		$\mathrm{SU}(2)[C_{8}]$
833.2.l.e	$833$	$2$	833.l	17.d	$8$	$40$	$10$	$6.652$		None		✓			833.2.l.d	$2$	$0$	$0$	$4$	$8$	$0$		$\mathrm{SU}(2)[C_{8}]$
833.2.l.f	$833$	$2$	833.l	17.d	$8$	$40$	$10$	$6.652$		None					119.2.q.a	$2$	$0$	$4$	$-4$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$
833.2.l.g	$833$	$2$	833.l	17.d	$8$	$40$	$10$	$6.652$		None					119.2.q.a	$2$	$0$	$4$	$4$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$

Decomposition of $S_{2}^{\mathrm{old}}(833, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(833, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(17, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(119, [\chi])$$^{\oplus 2}$