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

• Label: 3024.1.bw
• Level: $3024$
• Weight: $1$
• Character orbit: 3024.bw
• Rep. character: $\chi_{3024}(415,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $576$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3024.bw (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(576\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	84	4	80
Cusp forms	12	4	8
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	0	4	0	0

Trace form

\( 4q - 2q^{5} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

Label	Dim.	\(A\)	Field	Image	CM	RM	Traces				$q$-expansion
							\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)
3024.1.bw.a	\(4\)	\(1.509\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(q-\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\zeta_{12}q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)