Properties

Label 855.1.g
Level $855$
Weight $1$
Character orbit 855.g
Rep. character $\chi_{855}(379,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 855.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(4\)

Dimensions

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

Total New Old
Modular forms 22 7 15
Cusp forms 14 5 9
Eisenstein series 8 2 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5 q - q^{4} + q^{5} + O(q^{10}) \) \( 5 q - q^{4} + q^{5} + 2 q^{11} + q^{16} - 3 q^{19} + 3 q^{20} + q^{25} - 4 q^{26} - 2 q^{44} + 5 q^{49} - 2 q^{55} + 2 q^{61} - 5 q^{64} + 4 q^{74} - q^{76} - 3 q^{80} - 4 q^{85} - 3 q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.1.g.a $1$ $0.427$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+2q^{11}+q^{16}+q^{19}+\cdots\)
855.1.g.b $2$ $0.427$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{285}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-iq^{5}+q^{16}-iq^{17}-q^{19}+\cdots\)
855.1.g.c $2$ $0.427$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{2}+q^{4}+q^{5}-\beta q^{10}+\beta q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(855, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)