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

• Label: 3024.1.dc
• Level: $3024$
• Weight: $1$
• Character orbit: 3024.dc
• Rep. character: $\chi_{3024}(2321,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $3$
• 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.dc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
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	152	8	144
Cusp forms	80	8	72
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	4	0

Trace form

\( 8 q + q^{7} + 2 q^{13} + 3 q^{19} - q^{37} + 8 q^{43} - q^{49} + q^{67} - 3 q^{73} - 3 q^{79} + 8 q^{85} + 4 q^{91}+O(q^{100}) \)

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.dc.a	$3024$	$1$	3024.dc	21.h	$6$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					189.1.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{7}-q^{13}-\zeta_{6}^{2}q^{19}-\zeta_{6}q^{25}+\cdots\)
3024.1.dc.b	$3024$	$1$	3024.dc	21.h	$6$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					756.1.bk.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}q^{7}+q^{13}+\zeta_{6}^{2}q^{19}-\zeta_{6}q^{25}+\cdots\)
3024.1.dc.c	$3024$	$1$	3024.dc	21.h	$6$	$4$	$2$	$1.509$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None			✓		1512.1.cu.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{17}+(1+\cdots)q^{19}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3024, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)