Properties

Label 3248.1.ei
Level $3248$
Weight $1$
Character orbit 3248.ei
Rep. character $\chi_{3248}(13,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $24$
Newform subspaces $2$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3248 = 2^{4} \cdot 7 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3248.ei (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3248 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3248, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 24 24 0
Eisenstein series 48 48 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q + 4 q^{4} + O(q^{10}) \) \( 24 q + 4 q^{4} + 14 q^{11} - 4 q^{16} - 10 q^{22} - 2 q^{29} + 14 q^{44} + 4 q^{49} - 4 q^{53} - 14 q^{56} + 2 q^{58} - 4 q^{63} + 4 q^{64} + 4 q^{67} - 14 q^{72} + 4 q^{74} + 4 q^{81} + 4 q^{86} - 4 q^{88} - 14 q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3248, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3248.1.ei.a 3248.ei 3248.di $12$ $1.621$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-7}) \) None 3248.1.ei.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{5}q^{2}+\zeta_{28}^{10}q^{4}-\zeta_{28}^{13}q^{7}+\cdots\)
3248.1.ei.b 3248.ei 3248.di $12$ $1.621$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-7}) \) None 3248.1.ei.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}-\zeta_{28}^{13}q^{7}+\cdots\)