Properties

Label 600.1.z
Level $600$
Weight $1$
Character orbit 600.z
Rep. character $\chi_{600}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $1$
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: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
600.1.z.a 600.z 600.z $8$ $0.299$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}+\cdots\)