Properties

Label 500.1.h
Level 500
Weight 1
Character orbit h
Rep. character \(\chi_{500}(99,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 1
Sturm bound 75
Trace bound 0

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Defining parameters

Level: \( N \) = \( 500 = 2^{2} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 500.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(75\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(500, [\chi])\).

Total New Old
Modular forms 48 32 16
Cusp forms 8 8 0
Eisenstein series 40 24 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\(8q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 8q^{49} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(500, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
500.1.h.a \(8\) \(0.250\) \(\Q(\zeta_{20})\) \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{8}-\zeta_{20}^{4}q^{9}+\cdots\)