Properties

Label 3024.1.dd
Level $3024$
Weight $1$
Character orbit 3024.dd
Rep. character $\chi_{3024}(1423,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $576$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3024.dd (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

\( 4q + 4q^{5} + O(q^{10}) \) \( 4q + 4q^{5} + 2q^{13} + 2q^{17} - 2q^{29} + 2q^{37} + 2q^{41} + 2q^{49} - 2q^{53} + 2q^{65} - 2q^{73} + 2q^{77} + 2q^{85} + 2q^{89} + 2q^{97} + O(q^{100}) \)

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.dd.a \(4\) \(1.509\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(4\) \(0\) \(q+q^{5}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{3}q^{11}+\zeta_{12}^{2}q^{13}+\cdots\)

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

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