Properties

Label 1083.1.l
Level $1083$
Weight $1$
Character orbit 1083.l
Rep. character $\chi_{1083}(62,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $12$
Newform subspaces $2$
Sturm bound $126$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1083.l (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(126\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1083, [\chi])\).

Total New Old
Modular forms 132 108 24
Cusp forms 12 12 0
Eisenstein series 120 96 24

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

\( 12 q + 6 q^{7} + O(q^{10}) \) \( 12 q + 6 q^{7} - 12 q^{39} - 6 q^{64} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1083, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1083.1.l.a 1083.l 57.l $6$ $0.540$ \(\Q(\zeta_{18})\) $D_{3}$ \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(0\) \(0\) \(3\) \(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\)
1083.1.l.b 1083.l 57.l $6$ $0.540$ \(\Q(\zeta_{18})\) $D_{3}$ \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(0\) \(0\) \(3\) \(q-\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\)