Properties

Label 400.1.x
Level 400
Weight 1
Character orbit x
Rep. character \(\chi_{400}(79,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 4
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
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 28 4 24
Cusp forms 4 4 0
Eisenstein series 24 0 24

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

\(4q \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut 5q^{85} \) \(\mathstrut +\mathstrut 3q^{89} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.x.a \(4\) \(0.200\) \(\Q(\zeta_{10})\) \(D_{10}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{5}-\zeta_{10}^{4}q^{9}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)