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Properties

Label 1027.1.b
Level $1027$
Weight $1$
Character orbit 1027.b
Rep. character $\chi_{1027}(1026,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $93$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1027 = 13 \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1027.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1027 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(93\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1027, [\chi])\).

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

\( 5 q - 5 q^{4} + 5 q^{9} + O(q^{10}) \) \( 5 q - 5 q^{4} + 5 q^{9} + 5 q^{16} + 10 q^{22} - 5 q^{25} - 5 q^{26} - 5 q^{36} - 10 q^{40} - 5 q^{49} + 10 q^{62} - 5 q^{64} - 5 q^{79} + 5 q^{81} - 10 q^{88} - 10 q^{92} + 10 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1027, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1027.1.b.a 1027.b 1027.b $1$ $0.513$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-1027}) \) \(\Q(\sqrt{13}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-q^{13}+q^{16}-2q^{23}+\cdots\)
1027.1.b.b 1027.b 1027.b $4$ $0.513$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-79}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)