Space of modular forms of level 1502, weight 2, and trivial character

• Label: 1502.2.a
• Level: $1502$
• Weight: $2$
• Character orbit: 1502.a
• Rep. character: $\chi_{1502}(1,\cdot)$
• Character field: $\Q$
• Dimension: $63$
• Newform subspaces: $8$
• Sturm bound: $376$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(376\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1502))\).

	Total	New	Old
Modular forms	190	63	127
Cusp forms	187	63	124
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.

\(2\)	\(751\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(13\)
\(+\)	\(-\)	$-$	\(19\)
\(-\)	\(+\)	$-$	\(18\)
\(-\)	\(-\)	$+$	\(13\)
Plus space		\(+\)	\(26\)
Minus space		\(-\)	\(37\)

Trace form

\( 63 q - q^{2} + 2 q^{3} + 63 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - q^{8} + 67 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1502))\) 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	751
1502.2.a.a	$1502$	$2$	1502.a	1.a	$1$	$1$	$1$	$11.994$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-2\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+4q^{7}+\cdots\)
1502.2.a.b	$1502$	$2$	1502.a	1.a	$1$	$1$	$1$	$11.994$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1502.2.a.c	$1502$	$2$	1502.a	1.a	$1$	$2$	$2$	$11.994$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-2+\beta )q^{5}+\cdots\)
1502.2.a.d	$1502$	$2$	1502.a	1.a	$1$	$2$	$2$	$11.994$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-1\)	\(2\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(-4+\cdots)q^{7}+\cdots\)
1502.2.a.e	$1502$	$2$	1502.a	1.a	$1$	$11$	$11$	$11.994$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-11\)	\(-4\)	\(1\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{10}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1502.2.a.f	$1502$	$2$	1502.a	1.a	$1$	$11$	$11$	$11.994$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(11\)	\(-11\)	\(-12\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots\)
1502.2.a.g	$1502$	$2$	1502.a	1.a	$1$	$16$	$16$	$11.994$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(16\)	\(13\)	\(4\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{8}q^{5}+(1+\cdots)q^{6}+\cdots\)
1502.2.a.h	$1502$	$2$	1502.a	1.a	$1$	$19$	$19$	$11.994$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(-19\)	\(6\)	\(2\)	\(13\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1502))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1502)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(751))\)\(^{\oplus 2}\)