Properties

Label 52.1.j
Level $52$
Weight $1$
Character orbit 52.j
Rep. character $\chi_{52}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 52.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(52, [\chi])\).

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

\( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} - q^{9} + q^{10} - q^{13} - q^{16} + q^{17} + 2 q^{18} + q^{20} - q^{26} + q^{29} - q^{32} - 2 q^{34} - q^{36} + q^{37} - 2 q^{40} + q^{41} + q^{45} - q^{49} + 2 q^{52} - 2 q^{53} + q^{58} + q^{61} + 2 q^{64} + q^{65} + q^{68} - q^{72} - 2 q^{73} + q^{74} + q^{80} - q^{81} + q^{82} - q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(52, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
52.1.j.a 52.j 52.j $2$ $0.026$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-1}) \) None 52.1.j.a \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)