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

• Label: 285.2.c
• Level: $285$
• Weight: $2$
• Character orbit: 285.c
• Rep. character: $\chi_{285}(229,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
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	20	24
Cusp forms	36	20	16
Eisenstein series	8	0	8

Trace form

\( 20 q - 24 q^{4} + 2 q^{5} + 4 q^{6} - 20 q^{9} + O(q^{10}) \)

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	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.c.a	$285$	$2$	285.c	5.b	$2$	$6$	$6$	$2.276$	6.0.350464.1	None		✓			285.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
285.2.c.b	$285$	$2$	285.c	5.b	$2$	$14$	$14$	$2.276$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓		285.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)

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

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