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Properties

Label 1859.1.d
Level $1859$
Weight $1$
Character orbit 1859.d
Rep. character $\chi_{1859}(1858,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $182$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1859.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(182\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1859, [\chi])\).

Total New Old
Modular forms 28 16 12
Cusp forms 14 6 8
Eisenstein series 14 10 4

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

\( 6 q - 2 q^{3} - 6 q^{4} + 4 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{3} - 6 q^{4} + 4 q^{9} + 2 q^{12} + 6 q^{16} + 2 q^{23} - 4 q^{25} - 4 q^{27} - 4 q^{36} - 2 q^{48} - 6 q^{49} - 2 q^{53} - 2 q^{55} - 6 q^{64} + 4 q^{69} + 6 q^{75} + 2 q^{81} - 2 q^{92} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1859.1.d.a 1859.d 143.d $6$ $0.928$ 6.0.153664.1 $D_{7}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{2}+\beta _{4})q^{3}-q^{4}-\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1859, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1859, [\chi]) \cong \)