Space of modular forms of level 1062, weight 2, and trivial character

• Label: 1062.2.a
• Level: $1062$
• Weight: $2$
• Character orbit: 1062.a
• Rep. character: $\chi_{1062}(1,\cdot)$
• Character field: $\Q$
• Dimension: $25$
• Newform subspaces: $16$
• Sturm bound: $360$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1062 = 2 \cdot 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1062.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(360\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1062))\).

	Total	New	Old
Modular forms	188	25	163
Cusp forms	173	25	148
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.

\(2\)	\(3\)	\(59\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(-\)	\(+\)	\(+\)	$-$	\(4\)
\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(8\)
Minus space			\(-\)	\(17\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1062))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	59
1062.2.a.a	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}+4q^{11}+\cdots\)
1062.2.a.b	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots\)
1062.2.a.c	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{7}-q^{8}+4q^{11}-2q^{13}+\cdots\)
1062.2.a.d	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-4q^{11}+4q^{13}+\cdots\)
1062.2.a.e	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots\)
1062.2.a.f	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
1062.2.a.g	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-2q^{10}+\cdots\)
1062.2.a.h	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-4q^{11}+\cdots\)
1062.2.a.i	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{7}+q^{8}-4q^{11}-2q^{13}+\cdots\)
1062.2.a.j	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+5q^{13}+\cdots\)
1062.2.a.k	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}+q^{13}+\cdots\)
1062.2.a.l	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots\)
1062.2.a.m	$1062$	$2$	1062.a	1.a	$1$	$2$	$2$	$8.480$	\(\Q(\sqrt{11}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta )q^{5}+4q^{7}+q^{8}+\cdots\)
1062.2.a.n	$1062$	$2$	1062.a	1.a	$1$	$3$	$3$	$8.480$	3.3.316.1	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1062.2.a.o	$1062$	$2$	1062.a	1.a	$1$	$4$	$4$	$8.480$	4.4.106272.1	None	✓	$1$	$0$	\(-4\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{3}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots\)
1062.2.a.p	$1062$	$2$	1062.a	1.a	$1$	$4$	$4$	$8.480$	4.4.106272.1	None	✓	$1$	$0$	\(4\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{3}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1062))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1062)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(354))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(531))\)\(^{\oplus 2}\)