Properties

Label 3584.1.cd
Level $3584$
Weight $1$
Character orbit 3584.cd
Rep. character $\chi_{3584}(13,\cdot)$
Character field $\Q(\zeta_{128})$
Dimension $64$
Newform subspaces $1$
Sturm bound $512$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3584.cd (of order \(128\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3584 \)
Character field: \(\Q(\zeta_{128})\)
Newform subspaces: \( 1 \)
Sturm bound: \(512\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3584, [\chi])\).

Total New Old
Modular forms 192 192 0
Cusp forms 64 64 0
Eisenstein series 128 128 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 64 0 0 0

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3584.1.cd.a 3584.cd 3584.bd $64$ $1.789$ \(\Q(\zeta_{128})\) $D_{128}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{128}^{59}q^{2}-\zeta_{128}^{54}q^{4}+\zeta_{128}^{63}q^{7}+\cdots\)