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

• Label: 3240.1.v
• Level: $3240$
• Weight: $1$
• Character orbit: 3240.v
• Rep. character: $\chi_{3240}(1297,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $648$
• Trace bound: $5$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	108	4	104
Cusp forms	12	4	8
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	4	0

Trace form

\( 4 q + 4 q^{25} + 4 q^{31} + 4 q^{37} + 4 q^{43} - 4 q^{55} + 4 q^{67} - 4 q^{97}+O(q^{100}) \)

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.v.a	$3240$	$1$	3240.v	5.c	$4$	$2$	$1$	$1.617$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		✓			3240.1.v.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-q^{5}+q^{11}+i q^{19}+(-i-1)q^{23}+\cdots\)
3240.1.v.b	$3240$	$1$	3240.v	5.c	$4$	$2$	$1$	$1.617$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		✓			3240.1.v.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+q^{5}-q^{11}+i q^{19}+(i+1)q^{23}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3240, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 2}\)