Properties

Label 1011.1.r
Level $1011$
Weight $1$
Character orbit 1011.r
Rep. character $\chi_{1011}(8,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $6$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1011 = 3 \cdot 337 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1011.r (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1011 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1011, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - q^{3} - q^{4} - 2 q^{7} - q^{9} + O(q^{10}) \) \( 6 q - q^{3} - q^{4} - 2 q^{7} - q^{9} - q^{12} - 2 q^{13} - q^{16} - 2 q^{19} + 5 q^{21} - q^{25} - q^{27} + 5 q^{28} - 2 q^{31} - q^{36} + 5 q^{37} - 2 q^{39} - 2 q^{43} - q^{48} - 3 q^{49} - 2 q^{52} - 2 q^{57} + 5 q^{61} - 2 q^{63} - q^{64} + 5 q^{67} - 2 q^{73} - q^{75} - 2 q^{76} + 5 q^{79} - q^{81} - 2 q^{84} + 10 q^{91} - 2 q^{93} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1011, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1011.1.r.a 1011.r 1011.r $6$ $0.505$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)