Space of modular forms of level 285, weight 2, and Character 285.i

• Label: 285.2.i
• Level: $285$
• Weight: $2$
• Character orbit: 285.i
• Rep. character: $\chi_{285}(106,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$285 = 3 \cdot 5 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	285.i (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$19$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$6$
Sturm bound:			$80$
Trace bound:			$2$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(285, [\chi])$.

	Total	New	Old
Modular forms	88	24	64
Cusp forms	72	24	48
Eisenstein series	16	0	16

Trace form

24 * q + 4 * q^3 - 10 * q^4 - 2 * q^6 + 8 * q^7 - 12 * q^9 + 2 * q^10 + 8 * q^11 - 24 * q^12 + 12 * q^14 + 4 * q^15 - 6 * q^16 - 12 * q^17 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 12 * q^25 + 40 * q^26 - 8 * q^27 + 28 * q^28 - 16 * q^31 + 20 * q^32 + 8 * q^33 - 26 * q^34 - 4 * q^35 - 10 * q^36 - 16 * q^37 - 20 * q^38 + 16 * q^39 + 12 * q^40 - 20 * q^41 - 8 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^46 - 12 * q^47 + 12 * q^48 + 48 * q^49 - 4 * q^51 - 32 * q^52 - 8 * q^53 - 2 * q^54 + 24 * q^56 + 20 * q^57 + 104 * q^58 + 4 * q^59 + 6 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 40 * q^64 - 48 * q^65 + 16 * q^66 + 8 * q^67 - 40 * q^68 - 16 * q^69 - 4 * q^70 - 8 * q^71 - 8 * q^73 + 36 * q^74 - 8 * q^75 - 60 * q^76 + 16 * q^77 - 12 * q^78 + 8 * q^79 - 16 * q^80 - 12 * q^81 + 60 * q^82 - 40 * q^83 - 8 * q^84 - 8 * q^85 - 20 * q^86 + 16 * q^87 + 16 * q^88 - 36 * q^89 + 2 * q^90 - 20 * q^91 + 56 * q^92 - 12 * q^93 + 68 * q^94 + 16 * q^95 + 44 * q^96 + 20 * q^97 - 64 * q^98 - 4 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(285, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
285.2.i.a	$285$	$2$	285.i	19.c	$3$	$2$	$1$	$2.276$	$\Q(\sqrt{-3})$	None		✓			285.2.i.a	$2$	$1$	$-2$	$-1$	$1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
285.2.i.b	$285$	$2$	285.i	19.c	$3$	$2$	$1$	$2.276$	$\Q(\sqrt{-3})$	None		✓			285.2.i.b	$2$	$0$	$0$	$-1$	$-1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
285.2.i.c	$285$	$2$	285.i	19.c	$3$	$2$	$1$	$2.276$	$\Q(\sqrt{-3})$	None		✓			285.2.i.c	$2$	$0$	$2$	$1$	$1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
285.2.i.d	$285$	$2$	285.i	19.c	$3$	$4$	$2$	$2.276$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			285.2.i.d	$2$	$0$	$-2$	$2$	$2$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\cdots$
285.2.i.e	$285$	$2$	285.i	19.c	$3$	$4$	$2$	$2.276$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			285.2.i.e	$2$	$0$	$1$	$-2$	$2$	$12$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
285.2.i.f	$285$	$2$	285.i	19.c	$3$	$10$	$5$	$2.276$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓		285.2.i.f	$2$	$0$	$1$	$5$	$-5$	$4$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{4}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(285, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(285, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(57, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(95, [\chi])$$^{\oplus 2}$