Properties

Label 775.1.z
Level $775$
Weight $1$
Character orbit 775.z
Rep. character $\chi_{775}(154,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $12$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 775.z (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

\( 12 q + 3 q^{4} - 15 q^{8} + 3 q^{9} + O(q^{10}) \) \( 12 q + 3 q^{4} - 15 q^{8} + 3 q^{9} + 3 q^{10} - 6 q^{14} - 3 q^{16} + 3 q^{20} + 3 q^{31} - 3 q^{35} - 3 q^{36} + 15 q^{38} - 3 q^{40} - 12 q^{49} + 3 q^{50} - 9 q^{56} + 12 q^{64} - 15 q^{67} - 3 q^{70} - 15 q^{72} + 6 q^{76} - 3 q^{81} + 12 q^{90} - 3 q^{95} + O(q^{100}) \)

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

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