Space of modular forms of level 1, weight 114, and trivial character

• Label: 1.114.a
• Level: $1$
• Weight: $114$
• 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:	\( k \)	\(=\)	\( 114 \)
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 \(M_{114}(\Gamma_0(1))\).

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

Trace form

\( 9 q + 4973724357874032 q^{2} - 1047822666262699970761104924 q^{3} + 57140122287714158706660944854495488 q^{4} - 3116148576934475303759287082847998426250 q^{5} - 8679197271676415971774420800017032303605312 q^{6} - 175592521264923853936268390919613238158926276408 q^{7} - 1152754689437068715781677022006928573086863264747520 q^{8} + 551049940125998155825143115188713609620516409643418677 q^{9} + O(q^{10}) \)

Decomposition of \(S_{114}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.114.a.a	$1$	$114$	1.a	1.a	$1$	$9$	$9$	$80.863$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(49\!\cdots\!32\)	\(-10\!\cdots\!24\)	\(-31\!\cdots\!50\)	\(-17\!\cdots\!08\)	$+$	$2^{144}\cdot 3^{48}\cdot 5^{19}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 19^{3}\cdot 23$	$\mathrm{SU}(2)$	\(q+(552636039763781+\beta _{1})q^{2}+\cdots\)