Properties

Label 1008.1.dd
Level $1008$
Weight $1$
Character orbit 1008.dd
Rep. character $\chi_{1008}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1008.dd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1008, [\chi])\).

Total New Old
Modular forms 28 4 24
Cusp forms 4 4 0
Eisenstein series 24 0 24

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

\( 4 q - 4 q^{5} + 2 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{5} + 2 q^{9} + 2 q^{13} - 2 q^{17} - 4 q^{21} + 2 q^{29} - 2 q^{33} + 2 q^{37} - 2 q^{41} - 2 q^{45} + 2 q^{49} + 2 q^{53} + 2 q^{57} - 2 q^{65} - 2 q^{69} - 2 q^{73} - 2 q^{77} - 2 q^{81} + 2 q^{85} - 2 q^{89} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.1.dd.a 1008.dd 252.al $4$ $0.503$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)