Properties

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

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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: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(52, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
52.1.j.a \(2\) \(0.026\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)