Properties

Label 77.1.j
Level 77
Weight 1
Character orbit j
Rep. character \(\chi_{77}(20,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 4
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 77 = 7 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 77.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(77, [\chi])\).

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

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

\(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 4q^{32} \) \(\mathstrut -\mathstrut 3q^{36} \) \(\mathstrut +\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut +\mathstrut q^{46} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut +\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 3q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut -\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut q^{77} \) \(\mathstrut +\mathstrut 3q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut q^{86} \) \(\mathstrut +\mathstrut q^{88} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(77, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
77.1.j.a \(4\) \(0.038\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)