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Properties

Label 1848.1.ce
Level $1848$
Weight $1$
Character orbit 1848.ce
Rep. character $\chi_{1848}(1517,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $384$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1848.ce (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1848 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1848, [\chi])\).

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

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

\( 8 q + 4 q^{4} + 4 q^{9} + 8 q^{15} - 4 q^{16} - 4 q^{22} - 12 q^{31} - 6 q^{33} + 8 q^{36} - 4 q^{42} - 4 q^{49} - 4 q^{58} + 4 q^{60} - 8 q^{64} + 4 q^{70} - 4 q^{81} - 2 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1848.1.ce.a 1848.ce 1848.be $4$ $0.922$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None 1848.1.ce.a \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}+\cdots\)
1848.1.ce.b 1848.ce 1848.be $4$ $0.922$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None 1848.1.ce.a \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}+\cdots\)