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Properties

Label 3871.1.t
Level $3871$
Weight $1$
Character orbit 3871.t
Rep. character $\chi_{3871}(766,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $373$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3871 = 7^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3871.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 553 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(373\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3871, [\chi])\).

Total New Old
Modular forms 22 14 8
Cusp forms 6 6 0
Eisenstein series 16 8 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 4 0

Trace form

\( 6 q + 2 q^{2} - 2 q^{8} + q^{9} + 2 q^{11} - 6 q^{16} + 3 q^{18} + 6 q^{22} + 3 q^{23} - 3 q^{25} - 2 q^{29} + 4 q^{37} + 8 q^{39} - 2 q^{43} + q^{46} - q^{50} - 8 q^{51} + 4 q^{53} + 8 q^{57} + 2 q^{58}+ \cdots + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(3871, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3871.1.t.a 3871.t 553.t $2$ $1.932$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-7}) \) None 553.1.p.a \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{8}-\zeta_{6}q^{9}-q^{11}-q^{16}+\cdots\)
3871.1.t.b 3871.t 553.t $4$ $1.932$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $S_{4}$ None None 553.1.p.b \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+\beta _{1}q^{6}-q^{8}+\beta _{2}q^{9}+\cdots\)