Space of modular forms of level 5052, weight 2, and trivial character

• Label: 5052.2.a
• Level: $5052$
• Weight: $2$
• Character orbit: 5052.a
• Rep. character: $\chi_{5052}(1,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $7$
• Sturm bound: $1688$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 5052 = 2^{2} \cdot 3 \cdot 421 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5052.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1688\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5052))\).

	Total	New	Old
Modular forms	850	70	780
Cusp forms	839	70	769
Eisenstein series	11	0	11

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

\(2\)	\(3\)	\(421\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(-\)	\(15\)
\(-\)	\(+\)	\(-\)	\(+\)	\(20\)
\(-\)	\(-\)	\(+\)	\(+\)	\(15\)
\(-\)	\(-\)	\(-\)	\(-\)	\(20\)
Plus space			\(+\)	\(35\)
Minus space			\(-\)	\(35\)

Trace form

\( 70 q - 4 q^{5} + 70 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5052))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	421
5052.2.a.a	$5052$	$2$	5052.a	1.a	$1$	$1$	$1$	$40.340$	\(\Q\)	None	✓	✓			5052.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
5052.2.a.b	$5052$	$2$	5052.a	1.a	$1$	$2$	$2$	$40.340$	\(\Q(\sqrt{5}) \)	None	✓	✓			5052.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+3\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
5052.2.a.c	$5052$	$2$	5052.a	1.a	$1$	$2$	$2$	$40.340$	\(\Q(\sqrt{5}) \)	None	✓	✓			5052.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2\beta q^{5}-\beta q^{7}+q^{9}-2q^{11}+\cdots\)
5052.2.a.d	$5052$	$2$	5052.a	1.a	$1$	$13$	$13$	$40.340$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓		5052.2.a.d	$1$	$0$	\(0\)	\(-13\)	\(1\)	\(8\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(1+\beta _{7})q^{7}+q^{9}-\beta _{9}q^{11}+\cdots\)
5052.2.a.e	$5052$	$2$	5052.a	1.a	$1$	$13$	$13$	$40.340$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓		5052.2.a.e	$1$	$1$	\(0\)	\(13\)	\(-2\)	\(-15\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+q^{9}+\cdots\)
5052.2.a.f	$5052$	$2$	5052.a	1.a	$1$	$19$	$19$	$40.340$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓		5052.2.a.f	$1$	$0$	\(0\)	\(19\)	\(6\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1-\beta _{6})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5052.2.a.g	$5052$	$2$	5052.a	1.a	$1$	$20$	$20$	$40.340$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	5052.2.a.g	$1$	$1$	\(0\)	\(-20\)	\(-6\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}-\beta _{14}q^{7}+q^{9}+\beta _{9}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5052))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5052)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(421))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(842))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1263))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2526))\)\(^{\oplus 2}\)