Space of modular forms of level 1, weight 122, and trivial character

• Label: 1.122.a
• Level: $1$
• Weight: $122$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 122 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{122}(\Gamma_0(1))\).

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

Trace form

\( 9 q - 2345005562254519728 q^{2} - 45298662406895255983997747004 q^{3} + 8462901481545657250924227818768095488 q^{4} - 1892628936004587162449482404208025942059050 q^{5} - 169155345437237254853213475765636376857034060992 q^{6} + 2195742607988216453868262401462060909846066161833992 q^{7} - 6498505205013969366907252193209867920059782603760087040 q^{8} + 7945503363883566160952357352391639075761121301070127960917 q^{9} + O(q^{10}) \)

Decomposition of \(S_{122}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.122.a.a	$1$	$122$	1.a	1.a	$1$	$9$	$9$	$92.717$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-23\!\cdots\!28\)	\(-45\!\cdots\!04\)	\(-18\!\cdots\!50\)	\(21\!\cdots\!92\)	$+$	$2^{145}\cdot 3^{53}\cdot 5^{20}\cdot 7^{8}\cdot 11^{6}\cdot 13^{2}\cdot 17^{2}$	$\mathrm{SU}(2)$	\(q+(-260556173583835525+\beta _{1}+\cdots)q^{2}+\cdots\)