Properties

Label 68.1.f
Level $68$
Weight $1$
Character orbit 68.f
Rep. character $\chi_{68}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 68 = 2^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 68.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(68, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 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 2 0 0 0

Trace form

\( 2 q - 2 q^{4} - 2 q^{5} + O(q^{10}) \) \( 2 q - 2 q^{4} - 2 q^{5} + 2 q^{10} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 2 q^{20} + 2 q^{29} - 2 q^{37} - 2 q^{40} + 2 q^{41} + 2 q^{45} - 2 q^{50} - 2 q^{58} - 2 q^{61} - 2 q^{64} + 2 q^{68} + 2 q^{72} + 2 q^{73} + 2 q^{74} - 2 q^{80} - 2 q^{81} + 2 q^{82} + 2 q^{85} + 2 q^{90} - 2 q^{97} + 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(68, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
68.1.f.a 68.f 68.f $2$ $0.034$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)