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Properties

Label 855.1.z
Level $855$
Weight $1$
Character orbit 855.z
Rep. character $\chi_{855}(94,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $4$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 855.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(855, [\chi])\).

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

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q - 8 q^{4} + O(q^{10}) \) \( 16 q - 8 q^{4} - 8 q^{16} - 8 q^{24} - 8 q^{25} - 16 q^{26} + 16 q^{30} - 8 q^{36} + 32 q^{44} - 8 q^{49} - 8 q^{54} + 16 q^{64} + 16 q^{66} - 16 q^{80} - 8 q^{95} + 8 q^{96} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(855, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.1.z.a 855.z 855.z $2$ $0.427$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-95}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
855.1.z.b 855.z 855.z $2$ $0.427$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-95}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
855.1.z.c 855.z 855.z $4$ $0.427$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{3}+(-1+\cdots)q^{4}+\cdots\)
855.1.z.d 855.z 855.z $8$ $0.427$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)