Space of modular forms of level 1, weight 42, and trivial character

• Label: 1.42.a
• Level: $1$
• Weight: $42$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	3	3	0
Eisenstein series	1	1	0

Trace form

\( 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 4970194114982976 q^{6} + 57878416258239192 q^{7} - 3555831711183237120 q^{8} + 13277004110931878919 q^{9} + O(q^{10}) \)

Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.42.a.a	$1$	$42$	1.a	1.a	$1$	$3$	$3$	$10.647$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-344688\)	\(-10820953044\)	\(-21\!\cdots\!50\)	\(57\!\cdots\!92\)	$+$	$2^{11}\cdot 3^{3}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(-114896+\beta _{1})q^{2}+(-3606984348+\cdots)q^{3}+\cdots\)