Properties

Label 3024.1.f
Level $3024$
Weight $1$
Character orbit 3024.f
Rep. character $\chi_{3024}(433,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3024.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
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 64 4 60
Cusp forms 28 4 24
Eisenstein series 36 0 36

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

\( 4q + q^{7} + O(q^{10}) \) \( 4q + q^{7} - 2q^{25} + 4q^{37} + 2q^{43} + q^{49} - 2q^{67} + 4q^{79} - 6q^{85} + 3q^{91} + O(q^{100}) \)

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.f.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(-\zeta_{6}+\cdots)q^{19}+\cdots\)
3024.1.f.b \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(D_{6}\) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(2\) \(q+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+q^{7}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{17}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)