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

• Label: 285.2.b
• Level: $285$
• Weight: $2$
• Character orbit: 285.b
• Rep. character: $\chi_{285}(284,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $80$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(80\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	44	44	0
Cusp forms	36	36	0
Eisenstein series	8	8	0

Trace form

\( 36 q - 44 q^{4} + 4 q^{6} - 4 q^{9} + O(q^{10}) \)

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.b.a	$285$	$2$	285.b	285.b	$2$	$4$	$4$	$2.276$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-3q^{6}+\cdots\)
285.2.b.b	$285$	$2$	285.b	285.b	$2$	$16$	$16$	$2.276$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	\(\Q(\sqrt{-95}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2+\beta _{7})q^{4}-\beta _{2}q^{5}+\cdots\)
285.2.b.c	$285$	$2$	285.b	285.b	$2$	$16$	$16$	$2.276$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)