Properties

Label 776.1.bp
Level $776$
Weight $1$
Character orbit 776.bp
Rep. character $\chi_{776}(3,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $16$
Newform subspaces $1$
Sturm bound $98$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 776 = 2^{3} \cdot 97 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 776.bp (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 776 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 1 \)
Sturm bound: \(98\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(776, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 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

\( 16 q + 8 q^{3} - 8 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{3} - 8 q^{9} - 8 q^{12} - 16 q^{27} + 8 q^{36} + 8 q^{66} - 8 q^{68} + 8 q^{73} - 24 q^{81} + 8 q^{86} + 16 q^{88} - 16 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(776, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
776.1.bp.a 776.bp 776.ap $16$ $0.387$ \(\Q(\zeta_{48})\) $D_{48}$ \(\Q(\sqrt{-2}) \) None \(0\) \(8\) \(0\) \(0\) \(q-\zeta_{48}^{19}q^{2}+(\zeta_{48}^{8}-\zeta_{48}^{18})q^{3}+\cdots\)