Space of modular forms of level 2736, weight 1, and Character 2736.b

• Label: 2736.1.b
• Level: $2736$
• Weight: $1$
• Character orbit: 2736.b
• Rep. character: $\chi_{2736}(2735,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2736.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 228 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2736, [\chi])\).

	Total	New	Old
Modular forms	40	12	28
Cusp forms	16	12	4
Eisenstein series	24	0	24

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2736.1.b.a	$2736$	$1$	2736.b	228.b	$2$	$4$	$4$	$1.365$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-19}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
2736.1.b.b	$2736$	$1$	2736.b	228.b	$2$	$8$	$8$	$1.365$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-19}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$		\(q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)