Space of modular forms of level 3024, weight 1, and Character 3024.cg

• Label: 3024.1.cg
• Level: $3024$
• Weight: $1$
• Character orbit: 3024.cg
• Rep. character: $\chi_{3024}(2161,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cg (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3024, [\chi])\).

	Total	New	Old
Modular forms	108	4	104
Cusp forms	36	4	32
Eisenstein series	72	0	72

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + q^{7} - 3 q^{19} - 2 q^{25} + 6 q^{31} + q^{37} - 4 q^{43} + q^{49} + q^{67} - 3 q^{73} + q^{79}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3024, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3024.1.cg.a	$3024$	$1$	3024.cg	7.d	$6$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None					756.1.z.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{7}+(-1+\zeta_{6}^{2})q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
3024.1.cg.b	$3024$	$1$	3024.cg	7.d	$6$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None					189.1.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3024, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)