Properties

Label 2548.1.q
Level $2548$
Weight $1$
Character orbit 2548.q
Rep. character $\chi_{2548}(263,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $3$
Sturm bound $392$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2548.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 364 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(392\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2548, [\chi])\).

Total New Old
Modular forms 40 24 16
Cusp forms 8 8 0
Eisenstein series 32 16 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 4 q^{4} + 8 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{4} + 8 q^{9} - 4 q^{16} - 4 q^{25} - 4 q^{36} + 4 q^{50} + 4 q^{53} - 8 q^{58} + 8 q^{64} - 4 q^{65} + 4 q^{74} + 8 q^{81} - 8 q^{85} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2548, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2548.1.q.a $2$ $1.272$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots\)
2548.1.q.b $2$ $1.272$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots\)
2548.1.q.c $4$ $1.272$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)