Properties

Label 639.1.d
Level $639$
Weight $1$
Character orbit 639.d
Rep. character $\chi_{639}(496,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 639 = 3^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 639.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 71 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(639, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 12 3 9
Eisenstein series 4 1 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q + q^{2} + 2 q^{4} + q^{5} + 2 q^{8} + O(q^{10}) \) \( 3 q + q^{2} + 2 q^{4} + q^{5} + 2 q^{8} - 2 q^{10} + q^{16} - q^{19} - 4 q^{20} + 2 q^{25} + q^{29} + 3 q^{32} - q^{37} - 5 q^{38} - 4 q^{40} - q^{43} + 3 q^{49} + 3 q^{50} - 2 q^{58} - 3 q^{71} - q^{73} - 5 q^{74} - 3 q^{76} - q^{79} - 2 q^{80} + q^{83} + 2 q^{86} + q^{89} + 2 q^{95} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(639, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
639.1.d.a $3$ $0.319$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None \(1\) \(0\) \(1\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(1+\beta _{2})q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(639, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(639, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(71, [\chi])\)\(^{\oplus 3}\)