Properties

Label 693.2.bn
Level 693
Weight 2
Character orbit bn
Rep. character \(\chi_{693}(263,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 184
Newform subspaces 1
Sturm bound 192
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 693.bn (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

\( 184q - 2q^{3} + 172q^{4} - 6q^{5} - 6q^{9} + O(q^{10}) \) \( 184q - 2q^{3} + 172q^{4} - 6q^{5} - 6q^{9} + 3q^{11} - 30q^{12} - 6q^{14} - 6q^{15} + 148q^{16} - 24q^{20} - 6q^{22} + 12q^{23} + 78q^{25} - 36q^{26} - 14q^{27} - 4q^{31} + 5q^{33} - 56q^{36} - 4q^{37} - 54q^{42} - 39q^{44} - 46q^{45} - 98q^{48} - 2q^{49} - 24q^{53} - 10q^{55} - 60q^{56} + 6q^{58} - 6q^{60} + 88q^{64} - 60q^{66} - 4q^{67} - 10q^{69} - 42q^{70} + 16q^{75} - 58q^{78} - 108q^{80} + 26q^{81} + 18q^{86} - 3q^{88} - 30q^{89} - 36q^{91} + 78q^{92} + 12q^{93} - 4q^{97} + 70q^{99} + O(q^{100}) \)

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.bn.a \(184\) \(5.534\) None \(0\) \(-2\) \(-6\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database