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

• Label: 890.2.d
• Level: $890$
• Weight: $2$
• Character orbit: 890.d
• Rep. character: $\chi_{890}(889,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $4$
• Sturm bound: $270$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$890 = 2 \cdot 5 \cdot 89$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	890.d (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$445$
Character field:			$\Q$
Newform subspaces:			$4$
Sturm bound:			$270$
Trace bound:			$3$
Distinguishing $T_p$:			$3$

Dimensions

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

	Total	New	Old
Modular forms	140	44	96
Cusp forms	132	44	88
Eisenstein series	8	0	8

Trace form

44 * q - 44 * q^4 + 4 * q^5 + 44 * q^9 + 4 * q^10 + 44 * q^16 - 4 * q^20 + 8 * q^21 + 8 * q^25 - 8 * q^34 - 44 * q^36 + 40 * q^39 - 4 * q^40 - 20 * q^45 + 36 * q^49 - 24 * q^55 - 44 * q^64 + 8 * q^69 - 64 * q^71 - 8 * q^79 + 4 * q^80 + 148 * q^81 - 8 * q^84 - 96 * q^85 - 44 * q^89 - 48 * q^91 - 64 * q^94 + 24 * 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.d.a	$890$	$2$	890.d	445.c	$2$	$2$	$2$	$7.107$	$\Q(\sqrt{-1})$	None		✓			890.2.d.a	$2$	$0$	$0$	$-2$	$-4$	$-4$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}-q^{4}+(i-2)q^{5}-i q^{6}+\cdots$
890.2.d.b	$890$	$2$	890.d	445.c	$2$	$2$	$2$	$7.107$	$\Q(\sqrt{-1})$	None		✓			890.2.d.a	$2$	$1$	$0$	$2$	$-4$	$4$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}-q^{4}+(i-2)q^{5}+i q^{6}+\cdots$
890.2.d.c	$890$	$2$	890.d	445.c	$2$	$4$	$4$	$7.107$	$\Q(i, \sqrt{10})$	None		✓			890.2.d.c	$4$	$0$	$0$	$0$	$4$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}-q^{4}+(1-2\beta _{1})q^{5}+\cdots$
890.2.d.d	$890$	$2$	890.d	445.c	$2$	$36$	$36$	$7.107$		None		✓	✓		890.2.d.d	$4$	$0$	$0$	$0$	$8$	$0$		$\mathrm{SU}(2)[C_{2}]$

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}$