Space of modular forms of level 1, weight 98, and trivial character

• Label: 1.98.a
• Level: $1$
• Weight: $98$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 98 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{98}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	7	7	0
Eisenstein series	1	1	0

Trace form

\( 7 q - 16697241085008 q^{2} + 100515854497394358147996 q^{3} + 163057083940695061811962902784 q^{4} - 3658387999529088680958306590731350 q^{5} - 30592714388364079315260992082788233536 q^{6} - 184642311743115370607493500489904481438408 q^{7} + 36028528195426625427479134330455698506199040 q^{8} + 34775775472129528349857305774273773877811641051 q^{9} + O(q^{10}) \)

Decomposition of \(S_{98}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.98.a.a	$1$	$98$	1.a	1.a	$1$	$7$	$7$	$59.585$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-16\!\cdots\!08\)	\(10\!\cdots\!96\)	\(-36\!\cdots\!50\)	\(-18\!\cdots\!08\)	$+$	$2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19$	$\mathrm{SU}(2)$	\(q+(-2385320155001+\beta _{1})q^{2}+\cdots\)