Properties

Label 1800.1.g
Level 1800
Weight 1
Character orbit g
Rep. character \(\chi_{1800}(451,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 3
Sturm bound 360
Trace bound 2

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 34 7 27
Cusp forms 10 4 6
Eisenstein series 24 3 21

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + O(q^{10}) \) \( 4q + 2q^{11} + 4q^{16} + 2q^{19} - 2q^{34} + 2q^{41} + 2q^{44} - 4q^{46} + 4q^{49} - 4q^{59} - 6q^{76} - 4q^{86} + 2q^{89} - 4q^{94} + O(q^{100}) \)

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.g.a \(1\) \(0.898\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}+q^{17}+\cdots\)
1800.1.g.b \(1\) \(0.898\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{11}+q^{16}-q^{17}+\cdots\)
1800.1.g.c \(2\) \(0.898\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{16}+q^{19}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)