Properties

Label 400.1.b
Level 400
Weight 1
Character orbit b
Rep. character \(\chi_{400}(351,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 60
Trace bound 0

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Defining parameters

Level: \( N \) = \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 400.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(400, [\chi])\).

Total New Old
Modular forms 19 1 18
Cusp forms 1 1 0
Eisenstein series 18 0 18

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\(q \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(400, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
400.1.b.a \(1\) \(0.200\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-2q^{29}-2q^{41}+q^{49}-2q^{61}+\cdots\)