Space of modular forms of level 1, weight 28, and trivial character

• Label: 1.28.a
• Level: $1$
• Weight: $28$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	3	3	0
Cusp forms	2	2	0
Eisenstein series	1	1	0

Trace form

\( 2 q - 8280 q^{2} - 1286280 q^{3} + 190623296 q^{4} + 5443587900 q^{5} + 86882873184 q^{6} - 175391963600 q^{7} - 3195032348160 q^{8} + 1235136554154 q^{9} + O(q^{10}) \)

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.28.a.a	$1$	$28$	1.a	1.a	$1$	$2$	$2$	$4.619$	\(\Q(\sqrt{18209}) \)	None	✓	$1$	$0$	\(-8280\)	\(-1286280\)	\(5443587900\)	\(-175391963600\)	$+$	$2^{3}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-4140-\beta )q^{2}+(-643140-192\beta )q^{3}+\cdots\)