Properties

Label 980.1.n
Level $980$
Weight $1$
Character orbit 980.n
Rep. character $\chi_{980}(129,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 980.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(980, [\chi])\).

Total New Old
Modular forms 52 4 48
Cusp forms 4 4 0
Eisenstein series 48 0 48

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

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

Trace form

\( 4 q + O(q^{10}) \) \( 4 q + 2 q^{11} - 4 q^{15} - 2 q^{25} - 4 q^{29} - 2 q^{39} - 2 q^{51} + 2 q^{65} + 8 q^{71} + 2 q^{79} + 2 q^{81} - 4 q^{85} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.1.n.a 980.n 35.i $2$ $0.489$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+q^{13}+\cdots\)
980.1.n.b 980.n 35.i $2$ $0.489$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-q^{13}+\cdots\)