Properties

Label 900.1.bh
Level 900
Weight 1
Character orbit bh
Rep. character \(\chi_{900}(287,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 16
Newforms 1
Sturm bound 180
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 900.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 300 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(900, [\chi])\).

Total New Old
Modular forms 80 16 64
Cusp forms 16 16 0
Eisenstein series 64 0 64

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

\( 16q + O(q^{10}) \) \( 16q + 4q^{13} + 4q^{16} - 20q^{34} + 4q^{37} - 4q^{40} - 4q^{52} - 4q^{58} - 4q^{73} + 4q^{82} - 20q^{85} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(900, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
900.1.bh.a \(16\) \(0.449\) \(\Q(\zeta_{40})\) \(D_{20}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+\zeta_{40}^{3}q^{5}+\cdots\)