Space of modular forms of level 1003, weight 2, and trivial character

• Label: 1003.2.a
• Level: $1003$
• Weight: $2$
• Character orbit: 1003.a
• Rep. character: $\chi_{1003}(1,\cdot)$
• Character field: $\Q$
• Dimension: $77$
• Newform subspaces: $10$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1003))\).

	Total	New	Old
Modular forms	92	77	15
Cusp forms	89	77	12
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.

\(17\)	\(59\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(18\)
\(+\)	\(-\)	$-$	\(22\)
\(-\)	\(+\)	$-$	\(20\)
\(-\)	\(-\)	$+$	\(17\)
Plus space		\(+\)	\(35\)
Minus space		\(-\)	\(42\)

Trace form

\( 77 q - q^{2} + 75 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{7} + 3 q^{8} + 77 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		17	59
1003.2.a.a	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(1\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-q^{4}+q^{5}-3q^{6}+q^{7}+\cdots\)
1003.2.a.b	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{4}-2q^{5}+2q^{7}+q^{9}+\cdots\)
1003.2.a.c	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1003.2.a.d	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{5}-2q^{7}-3q^{9}+\cdots\)
1003.2.a.e	$1003$	$2$	1003.a	1.a	$1$	$3$	$3$	$8.009$	3.3.229.1	None	✓	$1$	$1$	\(-3\)	\(2\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{2})q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1003.2.a.f	$1003$	$2$	1003.a	1.a	$1$	$4$	$4$	$8.009$	4.4.2225.1	None	✓	$1$	$1$	\(-3\)	\(-2\)	\(1\)	\(8\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1003.2.a.g	$1003$	$2$	1003.a	1.a	$1$	$10$	$10$	$8.009$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-7\)	\(-12\)	\(-9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{8}q^{2}+(-1+\beta _{1})q^{3}+(2-\beta _{5})q^{4}+\cdots\)
1003.2.a.h	$1003$	$2$	1003.a	1.a	$1$	$16$	$16$	$8.009$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(-7\)	\(-21\)	\(-11\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1003.2.a.i	$1003$	$2$	1003.a	1.a	$1$	$18$	$18$	$8.009$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(5\)	\(1\)	\(21\)	\(-1\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1003.2.a.j	$1003$	$2$	1003.a	1.a	$1$	$22$	$22$	$8.009$		None	✓	$1$	$0$	\(5\)	\(7\)	\(19\)	\(3\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)