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Properties

Label 2793.1.bs
Level $2793$
Weight $1$
Character orbit 2793.bs
Rep. character $\chi_{2793}(398,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $12$
Newform subspaces $2$
Sturm bound $373$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2793.bs (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2793 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 2 \)
Sturm bound: \(373\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2793, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 12 12 0
Eisenstein series 24 24 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 2 q^{4} - 2 q^{7} - 2 q^{9} - 2 q^{16} + 2 q^{25} + 2 q^{28} + 2 q^{36} - 10 q^{39} + 4 q^{43} - 2 q^{49} - 2 q^{57} + 14 q^{61} + 12 q^{63} + 2 q^{64} - 2 q^{81} + 4 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(2793, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2793.1.bs.a 2793.bs 2793.as $6$ $1.394$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-3}) \) None 2793.1.bs.a \(0\) \(-1\) \(0\) \(-1\) \(q-\zeta_{14}^{5}q^{3}+\zeta_{14}q^{4}+\zeta_{14}^{4}q^{7}-\zeta_{14}^{3}q^{9}+\cdots\)
2793.1.bs.b 2793.bs 2793.as $6$ $1.394$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-3}) \) None 2793.1.bs.a \(0\) \(1\) \(0\) \(-1\) \(q+\zeta_{14}^{5}q^{3}+\zeta_{14}q^{4}+\zeta_{14}^{4}q^{7}-\zeta_{14}^{3}q^{9}+\cdots\)