Space of modular forms of level 1, weight 86, and trivial character

• Label: 1.86.a
• Level: $1$
• Weight: $86$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 86 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(7\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{86}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	6	6	0
Eisenstein series	1	1	0

Trace form

\( 6 q - 3596910688800 q^{2} - 158574346104614272200 q^{3} + 140991407339885551387640832 q^{4} - 937371071374809475998758615100 q^{5} - 2163199670798237803919272036318848 q^{6} + 376764526445862177226143056468406000 q^{7} + 444573639427992844351424894916577689600 q^{8} + 57207108743130009711910898489373895669038 q^{9} + O(q^{10}) \)

Decomposition of \(S_{86}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.86.a.a	$1$	$86$	1.a	1.a	$1$	$6$	$6$	$45.755$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-35\!\cdots\!00\)	\(-15\!\cdots\!00\)	\(-93\!\cdots\!00\)	\(37\!\cdots\!00\)	$+$	$2^{65}\cdot 3^{23}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17^{2}$	$\mathrm{SU}(2)$	\(q+(-599485114800+\beta _{1})q^{2}+\cdots\)