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
Newform subspaces 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: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(77, [\chi])\) into newform subspaces

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 \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)