Properties

Label 855.1.m
Level $855$
Weight $1$
Character orbit 855.m
Rep. character $\chi_{855}(512,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $2$
Sturm bound $120$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 855.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(7\)

Dimensions

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

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

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + O(q^{10}) \) \( 8 q - 8 q^{16} + 8 q^{43} - 8 q^{73} + O(q^{100}) \)

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.m.a 855.m 285.j $4$ $0.427$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots\)
855.1.m.b 855.m 285.j $4$ $0.427$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+(1+\zeta_{8}^{2})q^{7}+\cdots\)