Properties

Label 1700.1.p
Level $1700$
Weight $1$
Character orbit 1700.p
Rep. character $\chi_{1700}(251,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $270$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1700.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(270\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 32 14 18
Cusp forms 8 2 6
Eisenstein series 24 12 12

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

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

Trace form

\( 2 q - 2 q^{4} + O(q^{10}) \) \( 2 q - 2 q^{4} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 2 q^{29} + 2 q^{37} + 2 q^{41} + 2 q^{58} - 2 q^{61} - 2 q^{64} - 2 q^{68} - 2 q^{72} - 2 q^{73} + 2 q^{74} - 2 q^{81} - 2 q^{82} + 2 q^{97} - 2 q^{98} + O(q^{100}) \)

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.p.a 1700.p 68.f $2$ $0.848$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}-iq^{9}+q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1700, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1700, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)