Properties

Label 884.1.ct
Level $884$
Weight $1$
Character orbit 884.ct
Rep. character $\chi_{884}(7,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $16$
Newform subspaces $1$
Sturm bound $126$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 884 = 2^{2} \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 884.ct (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 884 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 1 \)
Sturm bound: \(126\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(884, [\chi])\).

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

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

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

Trace form

\( 16 q + O(q^{10}) \) \( 16 q + 8 q^{26} - 16 q^{29} - 8 q^{41} + 8 q^{45} - 8 q^{53} - 8 q^{72} + 8 q^{74} - 8 q^{90} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(884, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
884.1.ct.a 884.ct 884.bt $16$ $0.441$ \(\Q(\zeta_{48})\) $D_{48}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{17}q^{2}-\zeta_{48}^{10}q^{4}+(\zeta_{48}^{2}-\zeta_{48}^{19}+\cdots)q^{5}+\cdots\)