Properties

Label 1800.1.cr
Level 1800
Weight 1
Character orbit cr
Rep. character \(\chi_{1800}(37,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 16
Newforms 1
Sturm bound 360
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1800.cr (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).

Total New Old
Modular forms 80 32 48
Cusp forms 16 16 0
Eisenstein series 64 16 48

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

\(16q \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1800.1.cr.a \(16\) \(0.898\) \(\Q(\zeta_{40})\) \(D_{20}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{40}^{19}q^{2}-\zeta_{40}^{18}q^{4}+\zeta_{40}^{9}q^{5}+\cdots\)