Space of modular forms of level 2880, weight 1, and Character 2880.j

• Label: 2880.1.j
• Level: $2880$
• Weight: $1$
• Character orbit: 2880.j
• Rep. character: $\chi_{2880}(1279,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2880.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2880, [\chi])\).

	Total	New	Old
Modular forms	76	5	71
Cusp forms	28	3	25
Eisenstein series	48	2	46

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q - q^{5} - q^{25} + 2 q^{29} + 2 q^{41} - 3 q^{49} + 6 q^{61} - 4 q^{85} - 2 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2880, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2880.1.j.a	$2880$	$1$	2880.j	20.d	$2$	$1$	$1$	$1.437$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)	✓				80.1.h.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{5}+q^{25}+2q^{29}+2q^{41}-q^{49}+\cdots\)
2880.1.j.b	$2880$	$1$	2880.j	20.d	$2$	$2$	$2$	$1.437$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{15}) \)			✓		180.1.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{5}-2 i q^{17}-q^{25}-q^{49}-2 i q^{53}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2880, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)