Properties

Label 1620.1.v
Level $1620$
Weight $1$
Character orbit 1620.v
Rep. character $\chi_{1620}(217,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $8$
Newform subspaces $2$
Sturm bound $324$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1620.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(324\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1620, [\chi])\).

Total New Old
Modular forms 152 8 144
Cusp forms 8 8 0
Eisenstein series 144 0 144

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 8 0

Trace form

\( 8 q + 4 q^{7} + O(q^{10}) \) \( 8 q + 4 q^{7} + 4 q^{25} - 4 q^{31} + 4 q^{67} + 8 q^{73} + 4 q^{85} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1620.1.v.a $4$ $0.808$ \(\Q(\zeta_{12})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{4}q^{11}+\cdots\)
1620.1.v.b $4$ $0.808$ \(\Q(\zeta_{12})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{4}q^{11}+\cdots\)