Properties

Label 200.1.g
Level 200
Weight 1
Character orbit g
Rep. character \(\chi_{200}(51,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 30
Trace bound 2

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Defining parameters

Level: \( N \) = \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 200.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 8 5 3
Cusp forms 2 2 0
Eisenstein series 6 3 3

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 newform subspaces

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