Properties

Label 2007.1.v
Level $2007$
Weight $1$
Character orbit 2007.v
Rep. character $\chi_{2007}(91,\cdot)$
Character field $\Q(\zeta_{74})$
Dimension $36$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2007 = 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2007.v (of order \(74\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 223 \)
Character field: \(\Q(\zeta_{74})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2007, [\chi])\).

Total New Old
Modular forms 180 72 108
Cusp forms 36 36 0
Eisenstein series 144 36 108

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 36 0 0 0

Trace form

\( 36 q + q^{4} + 2 q^{7} + O(q^{10}) \) \( 36 q + q^{4} + 2 q^{7} - q^{16} - 2 q^{19} - q^{25} - 2 q^{28} + 2 q^{31} - 2 q^{37} - 2 q^{43} - 3 q^{49} + q^{64} + 2 q^{73} + 2 q^{76} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2007, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2007.1.v.a 2007.v 223.f $36$ $1.002$ \(\Q(\zeta_{74})\) $D_{74}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{74}^{20}q^{4}+(\zeta_{74}^{21}+\zeta_{74}^{27})q^{7}+\cdots\)