Space of modular forms of level 1007, weight 2, and trivial character

• Label: 1007.2.a
• Level: $1007$
• Weight: $2$
• Character orbit: 1007.a
• Rep. character: $\chi_{1007}(1,\cdot)$
• Character field: $\Q$
• Dimension: $79$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1007 = 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1007.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1007))\).

	Total	New	Old
Modular forms	92	79	13
Cusp forms	89	79	10
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.

\(19\)	\(53\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(13\)
\(+\)	\(-\)	$-$	\(28\)
\(-\)	\(+\)	$-$	\(26\)
\(-\)	\(-\)	$+$	\(12\)
Plus space		\(+\)	\(25\)
Minus space		\(-\)	\(54\)

Trace form

\( 79 q + 3 q^{2} + 4 q^{3} + 85 q^{4} - 8 q^{6} + 6 q^{7} + 3 q^{8} + 75 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		19	53
1007.2.a.a	$1007$	$2$	1007.a	1.a	$1$	$1$	$1$	$8.041$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots\)
1007.2.a.b	$1007$	$2$	1007.a	1.a	$1$	$12$	$12$	$8.041$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(1\)	\(-4\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
1007.2.a.c	$1007$	$2$	1007.a	1.a	$1$	$12$	$12$	$8.041$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(-5\)	\(-2\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
1007.2.a.d	$1007$	$2$	1007.a	1.a	$1$	$26$	$26$	$8.041$		None	✓	$1$	$0$	\(6\)	\(9\)	\(4\)	\(8\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1007.2.a.e	$1007$	$2$	1007.a	1.a	$1$	$28$	$28$	$8.041$		None	✓	$1$	$0$	\(3\)	\(-1\)	\(5\)	\(15\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)