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

\( 24 q + 4 q^{3} - 10 q^{4} - 2 q^{6} + 8 q^{7} - 12 q^{9} + O(q^{10}) \)

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

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

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