Properties

Label 2548.1.bn
Level $2548$
Weight $1$
Character orbit 2548.bn
Rep. character $\chi_{2548}(295,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $392$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2548.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(392\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 44 26 18
Cusp forms 12 6 6
Eisenstein series 32 20 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{8} - 3 q^{9} + O(q^{10}) \) \( 6 q + q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{8} - 3 q^{9} - q^{10} + q^{13} - 3 q^{16} - q^{17} - 2 q^{18} - q^{20} + 8 q^{25} + q^{26} - q^{29} + q^{32} + 2 q^{34} - 3 q^{36} - q^{37} + 2 q^{40} - q^{41} - q^{45} + 4 q^{50} - 2 q^{52} - 6 q^{53} + 3 q^{58} - q^{61} + 6 q^{64} + 7 q^{65} - q^{68} + q^{72} + 2 q^{73} + 3 q^{74} - q^{80} - 3 q^{81} - q^{82} - 7 q^{85} + 2 q^{89} + 2 q^{90} + 2 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2548.1.bn.a 2548.bn 52.j $2$ $1.272$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(2\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots\)
2548.1.bn.b 2548.bn 52.j $4$ $1.272$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2548, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2548, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 3}\)