Properties

Label 1859.1.c
Level $1859$
Weight $1$
Character orbit 1859.c
Rep. character $\chi_{1859}(846,\cdot)$
Character field $\Q$
Dimension $10$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
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 24 21 3
Cusp forms 10 10 0
Eisenstein series 14 11 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

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

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.c.a 1859.c 11.b $3$ $0.928$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
1859.1.c.b 1859.c 11.b $3$ $0.928$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots\)
1859.1.c.c 1859.c 11.b $4$ $0.928$ \(\Q(i, \sqrt{5})\) $D_{5}$ \(\Q(\sqrt{-143}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots\)