Space of modular forms of level 1, weight 90, and trivial character

• Label: 1.90.a
• Level: $1$
• Weight: $90$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 90 \)
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 \(M_{90}(\Gamma_0(1))\).

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

Trace form

\( 7 q - 31407330351408 q^{2} - 1359636564127989407364 q^{3} + 2261776677705673116713576704 q^{4} + 10232470009089362495458987082250 q^{5} - 47224471979937892179333042051869376 q^{6} + 38501341543555466088619988316514959992 q^{7} - 17954070319777658933153680910224754257920 q^{8} + 5642786905031106277764534052585801627237371 q^{9} + O(q^{10}) \)

Decomposition of \(S_{90}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.90.a.a	$1$	$90$	1.a	1.a	$1$	$7$	$7$	$50.162$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-31\!\cdots\!08\)	\(-13\!\cdots\!64\)	\(10\!\cdots\!50\)	\(38\!\cdots\!92\)	$+$	$2^{83}\cdot 3^{29}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2}$	$\mathrm{SU}(2)$	\(q+(-4486761478773-\beta _{1})q^{2}+\cdots\)