Properties

Label 3024.1.eg
Level $3024$
Weight $1$
Character orbit 3024.eg
Rep. character $\chi_{3024}(53,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
Newform subspaces $2$
Sturm bound $576$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3024.eg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(10\)

Dimensions

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

Total New Old
Modular forms 80 16 64
Cusp forms 32 16 16
Eisenstein series 48 0 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 16 0

Trace form

\( 16 q + O(q^{10}) \) \( 16 q - 4 q^{10} - 8 q^{13} + 8 q^{16} + 12 q^{28} + 12 q^{31} - 4 q^{37} + 8 q^{43} - 8 q^{46} - 4 q^{49} - 4 q^{52} + 4 q^{58} - 4 q^{61} - 4 q^{67} - 16 q^{76} - 8 q^{79} - 4 q^{88} + 4 q^{91} + 4 q^{94} + 8 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3024.1.eg.a 3024.eg 336.at $8$ $1.509$ \(\Q(\zeta_{24})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
3024.1.eg.b 3024.eg 336.at $8$ $1.509$ \(\Q(\zeta_{24})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{10}q^{7}+\cdots\)

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

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