Properties

Label 1800.1.r
Level 1800
Weight 1
Character orbit r
Rep. character \(\chi_{1800}(107,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newforms 2
Sturm bound 360
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1800.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 120 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(360\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 80 8 72
Cusp forms 32 8 24
Eisenstein series 48 0 48

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + O(q^{10}) \) \( 8q - 8q^{16} + 16q^{91} + O(q^{100}) \)

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.r.a \(4\) \(0.898\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2})q^{7}+\cdots\)
1800.1.r.b \(4\) \(0.898\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)