Properties

Label 693.2.bj
Level 693
Weight 2
Character orbit bj
Rep. character \(\chi_{693}(76,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 184
Newform subspaces 1
Sturm bound 192
Trace bound 0

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Defining parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 693.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 693 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(693, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184q + 84q^{4} + O(q^{10}) \) \( 184q + 84q^{4} - 10q^{14} - 24q^{15} - 76q^{16} - 10q^{22} - 16q^{23} + 72q^{25} - 24q^{36} - 16q^{37} + 10q^{42} + 60q^{44} - 2q^{49} + 32q^{53} + 40q^{56} - 44q^{58} - 120q^{60} - 128q^{64} - 4q^{67} - 20q^{70} + 16q^{71} - 4q^{77} + 68q^{78} - 8q^{81} - 12q^{86} + 34q^{88} + 20q^{91} + 64q^{92} - 32q^{93} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
693.2.bj.a \(184\) \(5.534\) None \(0\) \(0\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database