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

• Label: 3240.1.p
• Level: $3240$
• Weight: $1$
• Character orbit: 3240.p
• Rep. character: $\chi_{3240}(1459,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $6$
• Sturm bound: $648$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3240.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(648\)
Trace bound:			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	46	16	30
Cusp forms	22	8	14
Eisenstein series	24	8	16

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

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

Trace form

\( 8 q + 8 q^{4} + 8 q^{16} + 8 q^{25} + 8 q^{49} + 8 q^{64} - 8 q^{91} - 8 q^{94}+O(q^{100}) \)

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.p.a	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None	✓	✓			3240.1.p.a	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
3240.1.p.b	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None	✓	✓			3240.1.p.a	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
3240.1.p.c	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None	✓	✓			3240.1.p.a	$2$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
3240.1.p.d	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None	✓	✓			3240.1.p.a	$2$	$0$	\(1\)	\(0\)	\(1\)	\(1\)	$1$		\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
3240.1.p.e	$3240$	$1$	3240.p	40.e	$2$	$2$	$2$	$1.617$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-10}) \)	None	✓	✓			3240.1.p.e	$4$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$		\(q-q^{2}+q^{4}+q^{5}-\beta q^{7}-q^{8}-q^{10}+\cdots\)
3240.1.p.f	$3240$	$1$	3240.p	40.e	$2$	$2$	$2$	$1.617$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-10}) \)	None	✓	✓			3240.1.p.e	$4$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3240, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)