Properties

Label 869.1.j
Level $869$
Weight $1$
Character orbit 869.j
Rep. character $\chi_{869}(157,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $20$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 869 = 11 \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 869.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 869 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(869, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(869, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
869.1.j.a \(20\) \(0.434\) \(\Q(\zeta_{50})\) \(D_{25}\) \(\Q(\sqrt{-79}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots\)