Space of modular forms of level 43, weight 10, and trivial character

• Label: 43.10.a
• Level: $43$
• Weight: $10$
• Character orbit: 43.a
• Rep. character: $\chi_{43}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(43))\).

	Total	New	Old
Modular forms	34	32	2
Cusp forms	32	32	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(43\)	Dim
\(+\)	\(15\)
\(-\)	\(17\)

Trace form

\( 32 q + 16 q^{2} - 148 q^{3} + 7764 q^{4} - 684 q^{5} + 6558 q^{6} - 9756 q^{7} + 20652 q^{8} + 204642 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(43))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		43
43.10.a.a	$43$	$10$	43.a	1.a	$1$	$15$	$15$	$22.147$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-32\)	\(-317\)	\(-4717\)	\(-9680\)		$+$	$+$	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(-21-\beta _{2})q^{3}+(6^{3}+\cdots)q^{4}+\cdots\)
43.10.a.b	$43$	$10$	43.a	1.a	$1$	$17$	$17$	$22.147$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(48\)	\(169\)	\(4033\)	\(-76\)		$-$	$-$	$2^{13}\cdot 3^{5}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{2}+(10-\beta _{3})q^{3}+(267-4\beta _{1}+\cdots)q^{4}+\cdots\)