Properties

Label 1700.1.n
Level $1700$
Weight $1$
Character orbit 1700.n
Rep. character $\chi_{1700}(599,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $270$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1700.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 340 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(270\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1700, [\chi])\).

Total New Old
Modular forms 28 12 16
Cusp forms 4 4 0
Eisenstein series 24 8 16

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

\( 4 q + 4 q^{4} + O(q^{10}) \) \( 4 q + 4 q^{4} + 4 q^{16} - 4 q^{29} + 4 q^{41} - 4 q^{61} + 4 q^{64} - 4 q^{74} - 4 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1700, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1700.1.n.a 1700.n 340.n $2$ $0.848$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+iq^{9}+q^{16}+iq^{17}+\cdots\)
1700.1.n.b 1700.n 340.n $2$ $0.848$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+iq^{9}+q^{16}-iq^{17}+\cdots\)