Properties

Label 1017.1.f
Level $1017$
Weight $1$
Character orbit 1017.f
Rep. character $\chi_{1017}(98,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $114$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1017 = 3^{2} \cdot 113 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1017.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 339 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(114\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1017, [\chi])\).

Total New Old
Modular forms 12 4 8
Cusp forms 4 4 0
Eisenstein series 8 0 8

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

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

Trace form

\( 4 q - 4 q^{4} + 4 q^{7} + O(q^{10}) \) \( 4 q - 4 q^{4} + 4 q^{7} - 4 q^{10} - 4 q^{16} - 4 q^{28} + 4 q^{34} - 4 q^{37} - 4 q^{43} - 4 q^{46} + 4 q^{64} - 4 q^{70} + 4 q^{79} + 4 q^{85} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1017, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1017.1.f.a 1017.f 339.e $4$ $0.508$ \(\Q(\zeta_{8})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(4\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}-\zeta_{8}q^{5}+q^{7}+\cdots\)