Properties

Label 1800.1.l
Level 1800
Weight 1
Character orbit l
Rep. character \(\chi_{1800}(1601,\cdot)\)
Character field \(\Q\)
Dimension 4
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.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
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 60 4 56
Cusp forms 12 4 8
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 0 0 4 0

Trace form

\( 4q + O(q^{10}) \) \( 4q + 4q^{19} + 4q^{31} + 4q^{61} - 4q^{91} + O(q^{100}) \)

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.l.a \(2\) \(0.898\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}-\beta q^{11}+q^{13}+\beta q^{17}+q^{19}+\cdots\)
1800.1.l.b \(2\) \(0.898\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\beta q^{11}-q^{13}-\beta q^{17}+q^{19}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)