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

• Label: 285.2.k
• Level: $285$
• Weight: $2$
• Character orbit: 285.k
• Rep. character: $\chi_{285}(77,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
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	72	16
Cusp forms	72	72	0
Eisenstein series	16	0	16

Trace form

72 * q - 4 * q^3 - 8 * q^6 - 8 * q^7 - 8 * q^10 + 16 * q^12 - 16 * q^13 - 16 * q^15 - 72 * q^16 - 8 * q^21 + 24 * q^22 - 24 * q^25 + 8 * q^27 + 8 * q^28 + 16 * q^30 + 16 * q^31 - 16 * q^33 + 8 * q^36 - 24 * q^37 + 24 * q^40 - 64 * q^42 - 16 * q^43 + 32 * q^46 - 12 * q^48 + 24 * q^51 + 72 * q^52 + 16 * q^55 - 72 * q^58 + 36 * q^60 - 64 * q^61 - 8 * q^63 + 40 * q^66 - 56 * q^67 + 64 * q^70 - 20 * q^72 + 40 * q^73 + 40 * q^75 + 16 * q^78 - 24 * q^81 - 88 * q^82 - 8 * q^85 + 168 * q^88 + 40 * q^90 - 32 * q^91 - 8 * q^93 - 48 * q^96 + 8 * q^97

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.k.a	$285$	$2$	285.k	15.e	$4$	$4$	$2$	$2.276$	\(\Q(\zeta_{12})\)	None		✓			285.2.k.a	$2$	$1$	\(-4\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+\cdots\)
285.2.k.b	$285$	$2$	285.k	15.e	$4$	$4$	$2$	$2.276$	\(\Q(\zeta_{12})\)	None		✓			285.2.k.a	$2$	$0$	\(4\)	\(0\)	\(4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
285.2.k.c	$285$	$2$	285.k	15.e	$4$	$28$	$14$	$2.276$		None		✓			285.2.k.c	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
285.2.k.d	$285$	$2$	285.k	15.e	$4$	$36$	$18$	$2.276$		None		✓	✓		285.2.k.d	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$