Properties

Label 600.1.z
Level 600
Weight 1
Character orbit z
Rep. character \(\chi_{600}(29,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 1
Sturm bound 120
Trace bound 0

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Defining parameters

Level: \( N \) = \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 600.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 600 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(600, [\chi])\).

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

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

\(8q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 10q^{42} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(600, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
600.1.z.a \(8\) \(0.299\) \(\Q(\zeta_{20})\) \(D_{10}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}+\cdots\)