Properties

Label 507.1.h
Level $507$
Weight $1$
Character orbit 507.h
Rep. character $\chi_{507}(23,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 507.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(507, [\chi])\).

Total New Old
Modular forms 30 22 8
Cusp forms 2 2 0
Eisenstein series 28 20 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + q^{3} + q^{4} - q^{9} + O(q^{10}) \) \( 2 q + q^{3} + q^{4} - q^{9} + 2 q^{12} - q^{16} - 2 q^{25} - 2 q^{27} + q^{36} - 2 q^{43} + q^{48} - q^{49} + 2 q^{61} - 2 q^{64} - q^{75} - 4 q^{79} - q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(507, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
507.1.h.a 507.h 39.h $2$ $0.253$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots\)