Properties

Label 160.1.p
Level 160
Weight 1
Character orbit p
Rep. character \(\chi_{160}(33,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newforms 1
Sturm bound 24
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 160.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(160, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 2 2 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 2 0 0 0

Trace form

\( 2q + O(q^{10}) \) \( 2q - 2q^{13} - 2q^{17} - 2q^{25} + 2q^{37} + 2q^{45} + 2q^{53} + 2q^{65} + 2q^{73} - 2q^{81} - 2q^{85} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(160, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
160.1.p.a \(2\) \(0.080\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\)