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Properties

Label 1083.1.h
Level $1083$
Weight $1$
Character orbit 1083.h
Rep. character $\chi_{1083}(68,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $126$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1083.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(126\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 46 34 12
Cusp forms 6 2 4
Eisenstein series 40 32 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + q^{3} - q^{4} - 2 q^{7} - q^{9} - 2 q^{12} - q^{13} - q^{16} - q^{21} - q^{25} - 2 q^{27} + q^{28} + 2 q^{31} - q^{36} + 2 q^{37} - 2 q^{39} + q^{43} + q^{48} - q^{52} + q^{61} + q^{63}+ \cdots + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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.h.a 1083.h 57.h $2$ $0.540$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(1\) \(0\) \(-2\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1083, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1083, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)