Properties

Label 2548.1.ch
Level $2548$
Weight $1$
Character orbit 2548.ch
Rep. character $\chi_{2548}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
Newform subspaces $1$
Sturm bound $392$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2548.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 364 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(392\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 80 48 32
Cusp forms 16 16 0
Eisenstein series 64 32 32

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

\( 16 q - 16 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{9} + 8 q^{16} + 8 q^{50} - 8 q^{58} - 8 q^{74} + 16 q^{81} - 8 q^{85} + O(q^{100}) \)

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.ch.a 2548.ch 364.bg $16$ $1.272$ \(\Q(\zeta_{48})\) $D_{24}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{22}q^{2}-\zeta_{48}^{20}q^{4}+(-\zeta_{48}^{9}+\cdots)q^{5}+\cdots\)