Space of modular forms of level 1, weight 118, and trivial character

• Label: 1.118.a
• Level: $1$
• Weight: $118$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 118 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{118}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	9	9	0
Eisenstein series	1	1	0

Trace form

\( 9 q + 40417036685158752 q^{2} + 10302905323878152966875623636 q^{3} + 679626474486553930371683615220261888 q^{4} + 38453607070720263635688515692568185914150 q^{5} - 4850209982284354841792124153951223028275738752 q^{6} - 33936637323452994043236135663221508618375503117208 q^{7} + 84807426568136809852447254974619690045330359678238720 q^{8} + 228322388396621838147039528942639942618778890580268310597 q^{9} + O(q^{10}) \)

Decomposition of \(S_{118}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.118.a.a	$1$	$118$	1.a	1.a	$1$	$9$	$9$	$86.689$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(40\!\cdots\!52\)	\(10\!\cdots\!36\)	\(38\!\cdots\!50\)	\(-33\!\cdots\!08\)	$+$	$2^{151}\cdot 3^{56}\cdot 5^{18}\cdot 7^{7}\cdot 11^{4}\cdot 13^{4}\cdot 17^{2}\cdot 19\cdot 23\cdot 29^{2}$	$\mathrm{SU}(2)$	\(q+(4490781853906528-\beta _{1})q^{2}+\cdots\)