Space of modular forms of level 1, weight 52, and trivial character

• Label: 1.52.a
• Level: $1$
• Weight: $52$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 52 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{52}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	5	5	0
Cusp forms	4	4	0
Eisenstein series	1	1	0

Trace form

\( 4 q + 32756040 q^{2} + 403863773040 q^{3} + 7978103470875712 q^{4} + 1214113112967557880 q^{5} - 108315680321506869792 q^{6} + 6566332044151252469600 q^{7} - 139242173294665691205120 q^{8} + 5074459491561912905852628 q^{9} + O(q^{10}) \)

Decomposition of \(S_{52}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.52.a.a	$1$	$52$	1.a	1.a	$1$	$4$	$4$	$16.473$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(32756040\)	\(403863773040\)	\(12\!\cdots\!80\)	\(65\!\cdots\!00\)	$+$	$2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17$	$\mathrm{SU}(2)$	\(q+(8189010+\beta _{1})q^{2}+(100965943260+\cdots)q^{3}+\cdots\)