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

• Label: 3240.1.bn
• Level: $3240$
• Weight: $1$
• Character orbit: 3240.bn
• Rep. character: $\chi_{3240}(1889,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $648$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3240.bn (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(648\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	120	8	112
Cusp forms	24	8	16
Eisenstein series	96	0	96

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

\( 8 q + 8 q^{19} + 8 q^{55} + 4 q^{61} + 4 q^{79} - 8 q^{91}+O(q^{100}) \)

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.bn.a	$3240$	$1$	3240.bn	45.h	$6$	$8$	$4$	$1.617$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None			✓	✓	1080.1.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{5}-\zeta_{24}^{2}q^{7}+(\zeta_{24}^{5}-\zeta_{24}^{11}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3240, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 4}\)