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Properties

Label 3679.1.o
Level $3679$
Weight $1$
Character orbit 3679.o
Rep. character $\chi_{3679}(1414,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $3$
Sturm bound $331$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3679 = 13 \cdot 283 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3679.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3679 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(331\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3679, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 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 6 0 0 0

Trace form

\( 6 q + 3 q^{4} - 3 q^{9} + O(q^{10}) \) \( 6 q + 3 q^{4} - 3 q^{9} - 3 q^{16} - 6 q^{25} + 3 q^{36} + 3 q^{49} - 6 q^{64} - 9 q^{71} + 6 q^{77} - 3 q^{81} - 3 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3679, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3679.1.o.a 3679.o 3679.o $2$ $1.836$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-283}) \) None 3679.1.o.a \(0\) \(0\) \(0\) \(-3\) \(q+\zeta_{6}q^{4}+(-1+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}+\cdots\)
3679.1.o.b 3679.o 3679.o $2$ $1.836$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-283}) \) None 3679.1.o.b \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}-\zeta_{6}q^{9}+(-1-\zeta_{6})q^{11}+\cdots\)
3679.1.o.c 3679.o 3679.o $2$ $1.836$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-283}) \) None 3679.1.o.c \(0\) \(0\) \(0\) \(3\) \(q+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)