Space of modular forms of level 1287, weight 2, and trivial character

• Label: 1287.2.a
• Level: $1287$
• Weight: $2$
• Character orbit: 1287.a
• Rep. character: $\chi_{1287}(1,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $17$
• Sturm bound: $336$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1287.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(336\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1287))\).

	Total	New	Old
Modular forms	176	50	126
Cusp forms	161	50	111
Eisenstein series	15	0	15

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

\(3\)	\(11\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(+\)	\(-\)	\(+\)	$-$	\(5\)
\(+\)	\(-\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(+\)	$-$	\(9\)
\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	$+$	\(6\)
\(-\)	\(-\)	\(-\)	$-$	\(11\)
Plus space			\(+\)	\(20\)
Minus space			\(-\)	\(30\)

Trace form

\( 50 q + 58 q^{4} + 6 q^{5} - 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1287))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11	13
1287.2.a.a	$1287$	$2$	1287.a	1.a	$1$	$1$	$1$	$10.277$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}-2q^{7}+3q^{8}-2q^{10}+\cdots\)
1287.2.a.b	$1287$	$2$	1287.a	1.a	$1$	$1$	$1$	$10.277$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-2q^{7}+q^{11}-q^{13}+\cdots\)
1287.2.a.c	$1287$	$2$	1287.a	1.a	$1$	$1$	$1$	$10.277$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-2q^{7}-3q^{8}-2q^{10}+\cdots\)
1287.2.a.d	$1287$	$2$	1287.a	1.a	$1$	$1$	$1$	$10.277$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}-q^{11}+q^{13}-q^{16}+\cdots\)
1287.2.a.e	$1287$	$2$	1287.a	1.a	$1$	$1$	$1$	$10.277$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
1287.2.a.f	$1287$	$2$	1287.a	1.a	$1$	$2$	$2$	$10.277$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+(1-\beta )q^{5}-2q^{7}-\beta q^{8}+\cdots\)
1287.2.a.g	$1287$	$2$	1287.a	1.a	$1$	$2$	$2$	$10.277$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
1287.2.a.h	$1287$	$2$	1287.a	1.a	$1$	$3$	$3$	$10.277$	3.3.148.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1287.2.a.i	$1287$	$2$	1287.a	1.a	$1$	$3$	$3$	$10.277$	3.3.148.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1287.2.a.j	$1287$	$2$	1287.a	1.a	$1$	$3$	$3$	$10.277$	3.3.564.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
1287.2.a.k	$1287$	$2$	1287.a	1.a	$1$	$4$	$4$	$10.277$	4.4.1957.1	None	✓	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1}-\beta _{2})q^{2}+(1+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1287.2.a.l	$1287$	$2$	1287.a	1.a	$1$	$4$	$4$	$10.277$	4.4.11344.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-6\)	\(6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1287.2.a.m	$1287$	$2$	1287.a	1.a	$1$	$4$	$4$	$10.277$	4.4.8468.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(2-\beta _{1})q^{4}-\beta _{3}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
1287.2.a.n	$1287$	$2$	1287.a	1.a	$1$	$4$	$4$	$10.277$	4.4.11344.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(6\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1287.2.a.o	$1287$	$2$	1287.a	1.a	$1$	$5$	$5$	$10.277$	5.5.368464.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1287.2.a.p	$1287$	$2$	1287.a	1.a	$1$	$5$	$5$	$10.277$	5.5.368464.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1287.2.a.q	$1287$	$2$	1287.a	1.a	$1$	$6$	$6$	$10.277$	6.6.194616205.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1287))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1287)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 2}\)