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Properties

Label 1067.1.b
Level $1067$
Weight $1$
Character orbit 1067.b
Rep. character $\chi_{1067}(1066,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $98$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1067 = 11 \cdot 97 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1067.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1067 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(98\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1067, [\chi])\).

Total New Old
Modular forms 7 7 0
Cusp forms 5 5 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5 q - 2 q^{3} + 5 q^{4} + 3 q^{9} + O(q^{10}) \) \( 5 q - 2 q^{3} + 5 q^{4} + 3 q^{9} - q^{11} - 2 q^{12} + 5 q^{16} + 5 q^{25} - 4 q^{27} - 2 q^{31} - 2 q^{33} + 3 q^{36} - q^{44} - 2 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{53} + 5 q^{64} - 2 q^{75} + q^{81} - 2 q^{89} - 4 q^{91} - 4 q^{93} - q^{97} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1067, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1067.1.b.a 1067.b 1067.b $1$ $0.533$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1067}) \) \(\Q(\sqrt{97}) \) \(0\) \(-2\) \(0\) \(0\) \(q-2q^{3}+q^{4}+3q^{9}-q^{11}-2q^{12}+\cdots\)
1067.1.b.b 1067.b 1067.b $1$ $0.533$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1067}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-q^{3}+q^{4}-2q^{7}+q^{11}-q^{12}+q^{13}+\cdots\)
1067.1.b.c 1067.b 1067.b $1$ $0.533$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1067}) \) None \(0\) \(-1\) \(0\) \(2\) \(q-q^{3}+q^{4}+2q^{7}+q^{11}-q^{12}-q^{13}+\cdots\)
1067.1.b.d 1067.b 1067.b $2$ $0.533$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-1067}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+q^{4}-q^{11}+q^{12}-\beta q^{13}+\cdots\)