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Properties

Label 799.1.c
Level $799$
Weight $1$
Character orbit 799.c
Rep. character $\chi_{799}(798,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
Sturm bound $72$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 13 13 0
Cusp forms 11 11 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 11 0 0 0

Trace form

\( 11 q + 7 q^{4} + q^{9} + O(q^{10}) \) \( 11 q + 7 q^{4} + q^{9} + 3 q^{16} - 2 q^{17} - 10 q^{18} + q^{25} - 10 q^{32} - 3 q^{36} + 10 q^{42} + 3 q^{47} + q^{49} - 8 q^{50} + 5 q^{51} - 4 q^{53} - 4 q^{55} - q^{64} - q^{68} - 10 q^{72} + 11 q^{81} + 6 q^{83} + 10 q^{84} - 4 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.c.a 799.c 799.c $1$ $0.399$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-47}) \), \(\Q(\sqrt{-799}) \) \(\Q(\sqrt{17}) \) \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+3q^{4}-4q^{8}+q^{9}+5q^{16}+\cdots\)
799.1.c.b 799.c 799.c $2$ $0.399$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-799}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-\beta q^{5}+q^{9}+\beta q^{11}+q^{16}+\cdots\)
799.1.c.c 799.c 799.c $4$ $0.399$ \(\Q(\zeta_{16})^+\) $D_{8}$ \(\Q(\sqrt{-799}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{3})q^{10}+\cdots\)
799.1.c.d 799.c 799.c $4$ $0.399$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-47}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{3}+\cdots\)