Properties

Label 2624.1.dr
Level $2624$
Weight $1$
Character orbit 2624.dr
Rep. character $\chi_{2624}(97,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $32$
Newform subspaces $2$
Sturm bound $336$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2624.dr (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 328 \)
Character field: \(\Q(\zeta_{40})\)
Newform subspaces: \( 2 \)
Sturm bound: \(336\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2624, [\chi])\).

Total New Old
Modular forms 224 32 192
Cusp forms 32 32 0
Eisenstein series 192 0 192

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32 q + 8 q^{9} + O(q^{10}) \) \( 32 q + 8 q^{9} - 8 q^{17} + 8 q^{33} + 8 q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2624, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2624.1.dr.a 2624.dr 328.af $16$ $1.310$ \(\Q(\zeta_{40})\) $D_{40}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{40}+\zeta_{40}^{14})q^{3}+(\zeta_{40}^{2}-\zeta_{40}^{8}+\cdots)q^{9}+\cdots\)
2624.1.dr.b 2624.dr 328.af $16$ $1.310$ \(\Q(\zeta_{40})\) $D_{40}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{40}-\zeta_{40}^{14})q^{3}+(\zeta_{40}^{2}-\zeta_{40}^{8}+\cdots)q^{9}+\cdots\)