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Properties

Label 775.1.w
Level $775$
Weight $1$
Character orbit 775.w
Rep. character $\chi_{775}(61,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $12$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 775.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(775, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 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 12 0 0 0

Trace form

\( 12 q - 3 q^{4} + 9 q^{8} - 3 q^{9} + O(q^{10}) \) \( 12 q - 3 q^{4} + 9 q^{8} - 3 q^{9} - 3 q^{10} - 6 q^{14} - 3 q^{16} - 3 q^{20} - 6 q^{28} - 3 q^{31} - 6 q^{32} - 3 q^{35} - 3 q^{36} + 9 q^{38} - 3 q^{40} - 6 q^{47} + 12 q^{49} - 3 q^{50} + 9 q^{56} + 6 q^{64} + 9 q^{67} - 3 q^{70} + 9 q^{72} - 6 q^{76} - 6 q^{80} - 3 q^{81} - 6 q^{82} + 12 q^{90} - 3 q^{95} - 6 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
775.1.w.a 775.w 775.w $4$ $0.387$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-31}) \) None \(3\) \(0\) \(-1\) \(-2\) \(q+(1-\zeta_{10})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2})q^{4}+\cdots\)
775.1.w.b 775.w 775.w $8$ $0.387$ \(\Q(\zeta_{15})\) $D_{15}$ \(\Q(\sqrt{-31}) \) None \(-3\) \(0\) \(1\) \(2\) \(q+(-\zeta_{30}^{5}-\zeta_{30}^{13})q^{2}+(-\zeta_{30}^{3}+\cdots)q^{4}+\cdots\)