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Properties

Label 1859.1.k
Level $1859$
Weight $1$
Character orbit 1859.k
Rep. character $\chi_{1859}(1374,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $3$
Sturm bound $182$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1859.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(182\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 48 40 8
Cusp forms 20 20 0
Eisenstein series 28 20 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + 4 q^{3} - 4 q^{4} - 6 q^{9} + O(q^{10}) \) \( 20 q + 4 q^{3} - 4 q^{4} - 6 q^{9} + 8 q^{12} - 8 q^{14} - 6 q^{16} + 2 q^{22} - 16 q^{27} + 2 q^{36} - 12 q^{38} - 2 q^{42} + 2 q^{48} - 4 q^{49} - 8 q^{53} + 2 q^{55} + 2 q^{56} + 16 q^{64} + 12 q^{66} + 4 q^{75} + 4 q^{77} - 2 q^{81} - 4 q^{82} - 4 q^{88} + 4 q^{92} + O(q^{100}) \)

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.k.a 1859.k 143.k $6$ $0.928$ 6.0.64827.1 $D_{7}$ \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+\beta _{4}q^{3}-\beta _{5}q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1859.1.k.b 1859.k 143.k $6$ $0.928$ 6.0.64827.1 $D_{7}$ \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(2\) \(0\) \(q+\beta _{4}q^{3}-\beta _{5}q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1859.1.k.c 1859.k 143.k $8$ $0.928$ 8.0.12960000.1 $D_{5}$ \(\Q(\sqrt{-143}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{6}-\beta _{7})q^{2}+(1-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)