Properties

Label 600.1.bj
Level 600
Weight 1
Character orbit bj
Rep. character \(\chi_{600}(221,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 2
Sturm bound 120
Trace bound 2

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Defining parameters

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

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

\(8q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 8q^{24} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 6q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.bj.a \(4\) \(0.299\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(-1\) \(-2\) \(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{5}+\cdots\)
600.1.bj.b \(4\) \(0.299\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(1\) \(-2\) \(q+\zeta_{10}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}q^{5}+\cdots\)