Space of modular forms of level 1503, weight 2, and trivial character

• Label: 1503.2.a
• Level: $1503$
• Weight: $2$
• Character orbit: 1503.a
• Rep. character: $\chi_{1503}(1,\cdot)$
• Character field: $\Q$
• Dimension: $69$
• Newform subspaces: $9$
• Sturm bound: $336$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1503 = 3^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1503.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(336\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1503))\).

	Total	New	Old
Modular forms	172	69	103
Cusp forms	165	69	96
Eisenstein series	7	0	7

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

\(3\)	\(167\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(14\)
\(+\)	\(-\)	$-$	\(14\)
\(-\)	\(+\)	$-$	\(26\)
\(-\)	\(-\)	$+$	\(15\)
Plus space		\(+\)	\(29\)
Minus space		\(-\)	\(40\)

Trace form

\( 69 q + 2 q^{2} + 70 q^{4} + 4 q^{5} - 2 q^{7} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1503))\) 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	167
1503.2.a.a	$1503$	$2$	1503.a	1.a	$1$	$1$	$1$	$12.002$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{5}+4q^{7}+3q^{8}-4q^{10}+\cdots\)
1503.2.a.b	$1503$	$2$	1503.a	1.a	$1$	$2$	$2$	$12.002$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2-\beta )q^{7}+\cdots\)
1503.2.a.c	$1503$	$2$	1503.a	1.a	$1$	$5$	$5$	$12.002$	5.5.38569.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots\)
1503.2.a.d	$1503$	$2$	1503.a	1.a	$1$	$5$	$5$	$12.002$	5.5.36497.1	None	✓	$1$	$0$	\(4\)	\(0\)	\(9\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(1+\beta _{1}-2\beta _{3}+\beta _{4})q^{4}+\cdots\)
1503.2.a.e	$1503$	$2$	1503.a	1.a	$1$	$8$	$8$	$12.002$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-7\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{3}+\beta _{5}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1503.2.a.f	$1503$	$2$	1503.a	1.a	$1$	$8$	$8$	$12.002$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
1503.2.a.g	$1503$	$2$	1503.a	1.a	$1$	$12$	$12$	$12.002$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-4\)	\(11\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{4}+\beta _{6}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1503.2.a.h	$1503$	$2$	1503.a	1.a	$1$	$14$	$14$	$12.002$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(0\)	\(-12\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{11}+\cdots)q^{5}+\cdots\)
1503.2.a.i	$1503$	$2$	1503.a	1.a	$1$	$14$	$14$	$12.002$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(6\)	\(0\)	\(12\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1503))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1503)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 2}\)