Space of modular forms of level 3240, weight 1, and Character 3240.bh

• Label: 3240.1.bh
• Level: $3240$
• Weight: $1$
• Character orbit: 3240.bh
• Rep. character: $\chi_{3240}(269,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $9$
• Sturm bound: $648$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3240.bh (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 360 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(648\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3240, [\chi])\).

	Total	New	Old
Modular forms	76	36	40
Cusp forms	28	28	0
Eisenstein series	48	8	40

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	28	0	0	0

Trace form

\( 28 q - 4 q^{10} - 8 q^{16} + 10 q^{34} + 4 q^{40} + 4 q^{46} - 2 q^{49} - 20 q^{55} - 12 q^{64} + 6 q^{70} - 6 q^{76} - 4 q^{79} + 4 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3240.1.bh.a	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-30}) \)	None					1080.1.i.a	$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+q^{8}+\cdots\)
3240.1.bh.b	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-30}) \)	None					1080.1.i.a	$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots\)
3240.1.bh.c	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-30}) \)	None					1080.1.i.a	$4$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots\)
3240.1.bh.d	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-30}) \)	None					1080.1.i.a	$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-q^{8}+\cdots\)
3240.1.bh.e	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None					1080.1.i.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3240.1.bh.f	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-6}) \)	None					1080.1.i.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
3240.1.bh.g	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None					1080.1.i.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
3240.1.bh.h	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	\(\Q(\zeta_{12})\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)					120.1.i.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
3240.1.bh.i	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-6}) \)	None					1080.1.i.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+(1+\cdots)q^{7}+\cdots\)