Properties

Label 1620.1.bf
Level $1620$
Weight $1$
Character orbit 1620.bf
Rep. character $\chi_{1620}(19,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $12$
Newform subspaces $2$
Sturm bound $324$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1620.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 540 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(324\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 108 36 72
Cusp forms 36 12 24
Eisenstein series 72 24 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + O(q^{10}) \) \( 12 q + 6 q^{14} + 6 q^{29} - 12 q^{41} - 6 q^{49} + 6 q^{56} - 6 q^{61} - 6 q^{64} + 12 q^{70} - 12 q^{80} + 12 q^{94} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1620.1.bf.a 1620.bf 540.af $6$ $0.808$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
1620.1.bf.b 1620.bf 540.af $6$ $0.808$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(3\) \(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(-\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)