Properties

Label 693.2.co
Level 693
Weight 2
Character orbit co
Rep. character \(\chi_{693}(61,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 736
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.co (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 693 \)
Character field: \(\Q(\zeta_{30})\)
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 800 800 0
Cusp forms 736 736 0
Eisenstein series 64 64 0

Trace form

\( 736q + 5q^{2} - 9q^{3} - 85q^{4} - 5q^{7} - 40q^{8} - 9q^{9} + O(q^{10}) \) \( 736q + 5q^{2} - 9q^{3} - 85q^{4} - 5q^{7} - 40q^{8} - 9q^{9} - 4q^{11} - 24q^{12} + 5q^{14} - 24q^{15} + 87q^{16} - 30q^{17} - 5q^{18} - 30q^{19} - 66q^{20} - 12q^{22} - 4q^{23} - 15q^{24} + 146q^{25} - 66q^{26} + 27q^{27} - 20q^{28} - 10q^{29} + 25q^{30} - 9q^{31} - 84q^{33} + 12q^{34} + 5q^{35} - 44q^{36} - 6q^{37} - 45q^{39} - 90q^{41} - 57q^{42} - q^{44} - 24q^{45} - 30q^{46} - 9q^{47} + 30q^{48} - 3q^{49} + 15q^{50} + 35q^{51} - 38q^{53} + 102q^{56} - 60q^{57} - 26q^{58} + 21q^{59} + 99q^{60} - 15q^{61} - 35q^{63} + 132q^{64} + 90q^{66} + 8q^{67} - 27q^{69} - 68q^{70} - 40q^{71} - 65q^{72} - 30q^{73} - 290q^{74} - 69q^{75} + 21q^{77} - 136q^{78} + 5q^{79} + 150q^{80} + 47q^{81} - 30q^{82} - 5q^{84} - 10q^{85} - 14q^{86} - 32q^{88} - 78q^{89} + 30q^{90} - 40q^{91} - 72q^{92} + 123q^{93} - 15q^{94} - 35q^{95} - 135q^{96} - 80q^{99} + O(q^{100}) \)

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.co.a \(736\) \(5.534\) None \(5\) \(-9\) \(0\) \(-5\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database