Properties

Label 799.1.e
Level $799$
Weight $1$
Character orbit 799.e
Rep. character $\chi_{799}(140,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 799.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 799 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(799, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q - 10 q^{4} + O(q^{10}) \) \( 10 q - 10 q^{4} - 10 q^{12} - 10 q^{14} + 10 q^{16} + 10 q^{24} - 10 q^{47} + 10 q^{48} + 10 q^{51} + 10 q^{54} + 10 q^{56} - 10 q^{63} - 10 q^{64} - 10 q^{68} - 10 q^{81} + 20 q^{84} - 10 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(799, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
799.1.e.a 799.e 799.e $2$ $0.399$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-47}) \) None \(0\) \(2\) \(0\) \(-2\) \(q-iq^{2}+(1-i)q^{3}-3q^{4}+(-2-2i+\cdots)q^{6}+\cdots\)
799.1.e.b 799.e 799.e $8$ $0.399$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-47}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}+(-\zeta_{20}+\zeta_{20}^{4}+\cdots)q^{3}+\cdots\)