Space of modular forms of level 3, weight 43, and Character 3.b

• Label: 3.43.b
• Level: $3$
• Weight: $43$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 43 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{43}(3, [\chi])\).

	Total	New	Old
Modular forms	15	15	0
Cusp forms	13	13	0
Eisenstein series	2	2	0

Trace form

\( 13 q + 6526851993 q^{3} - 30601457050784 q^{4} - 47900661722006688 q^{6} + 104431479090834554 q^{7} + 98939492749372360149 q^{9} + O(q^{10}) \)

Decomposition of \(S_{43}^{\mathrm{new}}(3, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.43.b.a	$3$	$43$	3.b	3.b	$2$	$1$	$1$	$33.518$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-10460353203\)	\(0\)	\(14\!\cdots\!86\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{21}q^{3}+2^{42}q^{4}+146246101081752386q^{7}+\cdots\)
3.43.b.b	$3$	$43$	3.b	3.b	$2$	$12$	$12$	$33.518$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(16987205196\)	\(0\)	\(-41\!\cdots\!32\)	$2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1415600433+546\beta _{1}+\cdots)q^{3}+\cdots\)