Properties

Label 799.1.h
Level $799$
Weight $1$
Character orbit 799.h
Rep. character $\chi_{799}(93,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $20$
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.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 799 \)
Character field: \(\Q(\zeta_{8})\)
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 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

\( 20q + O(q^{10}) \) \( 20q - 20q^{16} - 20q^{24} - 20q^{42} + 20q^{48} - 20q^{51} + 20q^{54} + 20q^{56} - 20q^{83} + 40q^{84} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
799.1.h.a \(4\) \(0.399\) \(\Q(\zeta_{8})\) \(D_{8}\) \(\Q(\sqrt{-47}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
799.1.h.b \(16\) \(0.399\) \(\Q(\zeta_{40})\) \(D_{40}\) \(\Q(\sqrt{-47}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(\zeta_{40}^{11}-\zeta_{40}^{19})q^{2}+(-\zeta_{40}^{7}+\zeta_{40}^{8}+\cdots)q^{3}+\cdots\)