Space of modular forms of level 890, weight 2, and Character 890.bb

• Label: 890.2.bb
• Level: $890$
• Weight: $2$
• Character orbit: 890.bb
• Rep. character: $\chi_{890}(7,\cdot)$
• Character field: $\Q(\zeta_{88})$
• Dimension: $1800$
• Newform subspaces: $2$
• Sturm bound: $270$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$890 = 2 \cdot 5 \cdot 89$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	890.bb (of order $88$ and degree $40$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$445$
Character field:			$\Q(\zeta_{88})$
Newform subspaces:			$2$
Sturm bound:			$270$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(890, [\chi])$.

	Total	New	Old
Modular forms	5560	1800	3760
Cusp forms	5240	1800	3440
Eisenstein series	320	0	320

Trace form

1800 * q + 8 * q^3 - 4 * q^5 - 8 * q^6 + 8 * q^9 - 8 * q^12 - 8 * q^13 + 8 * q^14 + 8 * q^15 + 180 * q^16 + 8 * q^21 - 144 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 32 * q^27 + 28 * q^29 + 16 * q^30 + 32 * q^33 + 20 * q^34 + 56 * q^35 - 8 * q^36 + 40 * q^37 + 16 * q^38 - 28 * q^41 + 32 * q^43 - 16 * q^44 - 48 * q^45 + 80 * q^48 + 16 * q^49 + 32 * q^51 - 12 * q^52 - 24 * q^54 - 8 * q^56 + 8 * q^58 + 96 * q^59 + 8 * q^60 - 20 * q^61 + 16 * q^63 - 72 * q^69 - 16 * q^70 + 16 * q^71 + 20 * q^72 - 84 * q^73 + 8 * q^74 - 32 * q^75 - 80 * q^76 + 632 * q^77 + 48 * q^79 + 4 * q^80 - 880 * q^81 - 36 * q^82 - 64 * q^83 + 8 * q^84 - 256 * q^85 - 104 * q^86 - 360 * q^87 + 32 * q^88 - 80 * q^89 - 304 * q^91 - 8 * q^92 - 96 * q^93 - 56 * q^94 + 32 * q^95 - 80 * q^96 - 80 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(890, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
890.2.bb.a	$890$	$2$	890.bb	445.aa	$88$	$880$	$22$	$7.107$		None		✓			890.2.y.a	$2$	$0$	$0$	$4$	$0$	$4$		$\mathrm{SU}(2)[C_{88}]$
890.2.bb.b	$890$	$2$	890.bb	445.aa	$88$	$920$	$23$	$7.107$		None		✓	✓		890.2.y.b	$2$	$0$	$0$	$4$	$-4$	$-4$		$\mathrm{SU}(2)[C_{88}]$

Decomposition of $S_{2}^{\mathrm{old}}(890, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(890, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(445, [\chi])$$^{\oplus 2}$