Space of modular forms of level 1, weight 112, and trivial character

• Label: 1.112.a
• Level: $1$
• Weight: $112$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 112 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{112}(\Gamma_0(1))\).

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

Trace form

\( 9 q + 7300500744476376 q^{2} + 233675452617241539765416652 q^{3} + 11020070169858572323722385321061952 q^{4} + 814194067724935025770916308591172296830 q^{5} - 21301527237484005705216688979545976184644832 q^{6} + 78389901636433627730832560362319405491179083256 q^{7} + 331917555337838634305814685721710111074446802593280 q^{8} + 448549390735821931740487725597506918142357121619864013 q^{9} + O(q^{10}) \)

Decomposition of \(S_{112}^{\mathrm{new}}(\Gamma_0(1))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.112.a.a	$1$	$112$	1.a	1.a	$1$	$9$	$9$	$78.026$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(73\!\cdots\!76\)	\(23\!\cdots\!52\)	\(81\!\cdots\!30\)	\(78\!\cdots\!56\)	$+$	$2^{135}\cdot 3^{56}\cdot 5^{16}\cdot 7^{7}\cdot 11^{3}\cdot 13\cdot 19\cdot 37^{3}$	$\mathrm{SU}(2)$	\(q+(811166749386264+\beta _{1})q^{2}+\cdots\)