Space of modular forms of level 1, weight 72, and trivial character

• Label: 1.72.a
• Level: $1$
• Weight: $72$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{72}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	6	6	0
Eisenstein series	1	1	0

Trace form

\( 6 q + 66157336440 q^{2} + 89896952777770440 q^{3} + 8215211164782426312768 q^{4} - 4278141122384906054186220 q^{5} - 3844185387092474097708129888 q^{6} + 339238077991027352510892027600 q^{7} + 261748255411117464004338054151680 q^{8} + 28987747971890967878679507858381342 q^{9} + O(q^{10}) \)

Decomposition of \(S_{72}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.72.a.a	$1$	$72$	1.a	1.a	$1$	$6$	$6$	$31.925$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(66157336440\)	\(89\!\cdots\!40\)	\(-42\!\cdots\!20\)	\(33\!\cdots\!00\)	$+$	$2^{55}\cdot 3^{20}\cdot 5^{6}\cdot 7^{3}$	$\mathrm{SU}(2)$	\(q+(11026222740-\beta _{1})q^{2}+(14982825462961740+\cdots)q^{3}+\cdots\)