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Properties

Label 3879.1.g
Level $3879$
Weight $1$
Character orbit 3879.g
Rep. character $\chi_{3879}(430,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $46$
Newform subspaces $3$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3879 = 3^{2} \cdot 431 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3879.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3879 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(432\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3879, [\chi])\).

Total New Old
Modular forms 50 50 0
Cusp forms 46 46 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 42 4 0 0

Trace form

\( 46 q + 2 q^{2} - 4 q^{3} - 21 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{8} + 4 q^{9} + O(q^{10}) \) \( 46 q + 2 q^{2} - 4 q^{3} - 21 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} - 2 q^{15} - 19 q^{16} + 2 q^{18} - 2 q^{22} - 2 q^{23} - 4 q^{24} - 21 q^{25} - 4 q^{27} + 2 q^{29} - 4 q^{30} - 2 q^{33} + 2 q^{40} + 2 q^{41} + 2 q^{45} - 4 q^{46} - 2 q^{48} - 21 q^{49} - 2 q^{54} + 4 q^{55} - 2 q^{58} + 2 q^{59} - 2 q^{61} + 46 q^{64} + 2 q^{66} + 2 q^{69} + 4 q^{72} + 4 q^{80} + 4 q^{81} + 4 q^{82} - 2 q^{87} + 2 q^{88} + 4 q^{90} - 4 q^{91} - 2 q^{97} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3879, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3879.1.g.a 3879.g 3879.g $4$ $1.936$ \(\Q(\zeta_{12})\) $A_{4}$ None None 3879.1.g.a \(2\) \(-4\) \(2\) \(0\) \(q-\zeta_{12}^{4}q^{2}-q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}^{4}q^{6}+\cdots\)
3879.1.g.b 3879.g 3879.g $6$ $1.936$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-431}) \) None 3879.1.g.b \(-6\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{8}q^{3}-3\zeta_{18}^{3}q^{4}+\cdots\)
3879.1.g.c 3879.g 3879.g $36$ $1.936$ \(\Q(\zeta_{63})\) $D_{63}$ \(\Q(\sqrt{-431}) \) None 3879.1.g.c \(6\) \(0\) \(0\) \(0\) \(q+(\zeta_{126}^{48}-\zeta_{126}^{57})q^{2}+\zeta_{126}^{4}q^{3}+\cdots\)