Properties

Label 200.1.e
Level 200
Weight 1
Character orbit e
Rep. character \(\chi_{200}(99,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 30
Trace bound 0

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Defining parameters

Level: \( N \) = \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 200.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 40 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(200, [\chi])\).

Total New Old
Modular forms 8 4 4
Cusp forms 2 2 0
Eisenstein series 6 2 4

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{4} - 2q^{6} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{6} - 2q^{11} + 2q^{16} + 2q^{19} + 2q^{24} + 2q^{34} - 2q^{41} + 2q^{44} - 2q^{49} + 2q^{51} - 2q^{54} - 4q^{59} - 2q^{64} + 2q^{66} - 2q^{76} - 2q^{81} + 4q^{86} + 2q^{89} - 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(200, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
200.1.e.a \(2\) \(0.100\) \(\Q(\sqrt{-1}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots\)