Space of modular forms of level 287, weight 2, and trivial character

• Label: 287.2.a
• Level: $287$
• Weight: $2$
• Character orbit: 287.a
• Rep. character: $\chi_{287}(1,\cdot)$
• Character field: $\Q$
• Dimension: $21$
• Newform subspaces: $6$
• Sturm bound: $56$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(56\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(287))\).

	Total	New	Old
Modular forms	30	21	9
Cusp forms	27	21	6
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)	\(41\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(+\)	$-$	\(8\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(4\)
Minus space		\(-\)	\(17\)

Trace form

\( 21 q + q^{2} + 17 q^{4} + 2 q^{5} + 4 q^{6} - q^{7} + 9 q^{8} + 25 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(287))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	41
287.2.a.a	$287$	$2$	287.a	1.a	$1$	$2$	$2$	$2.292$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
287.2.a.b	$287$	$2$	287.a	1.a	$1$	$2$	$2$	$2.292$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
287.2.a.c	$287$	$2$	287.a	1.a	$1$	$3$	$3$	$2.292$	3.3.257.1	None	✓	$1$	$0$	\(1\)	\(-1\)	\(6\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
287.2.a.d	$287$	$2$	287.a	1.a	$1$	$3$	$3$	$2.292$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(4\)	\(5\)	\(2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(2-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
287.2.a.e	$287$	$2$	287.a	1.a	$1$	$5$	$5$	$2.292$	5.5.633117.1	None	✓	$1$	$0$	\(-1\)	\(4\)	\(-5\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
287.2.a.f	$287$	$2$	287.a	1.a	$1$	$6$	$6$	$2.292$	6.6.185257757.1	None	✓	$1$	$0$	\(-1\)	\(-4\)	\(-1\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(287))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(287)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 2}\)