Properties

Label 693.2.cb
Level 693
Weight 2
Character orbit cb
Rep. character \(\chi_{693}(74,\cdot)\)
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.cb (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

\( 736q - 3q^{3} - 182q^{4} - 9q^{5} - 20q^{6} - 5q^{7} - 9q^{9} + O(q^{10}) \) \( 736q - 3q^{3} - 182q^{4} - 9q^{5} - 20q^{6} - 5q^{7} - 9q^{9} - 18q^{11} + 20q^{12} - 10q^{13} - 9q^{14} - 24q^{15} - 158q^{16} - 5q^{18} - 10q^{19} - 36q^{20} - 4q^{22} - 42q^{23} + 35q^{24} - 73q^{25} - 24q^{26} - 21q^{27} - 20q^{28} - 30q^{29} - 35q^{30} - 6q^{31} + 40q^{33} - 20q^{34} + 75q^{35} + 36q^{36} - 6q^{37} - 15q^{38} - 45q^{39} + 45q^{40} - 30q^{41} - 71q^{42} + 39q^{44} + 36q^{45} + 10q^{46} - 52q^{48} - 3q^{49} - 105q^{50} + 75q^{51} + 5q^{52} - 36q^{53} - 30q^{55} + 30q^{56} - 60q^{57} + 29q^{58} + 121q^{60} - 10q^{61} - 105q^{63} - 148q^{64} - 25q^{66} - 16q^{67} - 15q^{68} + 105q^{69} - 33q^{70} - 125q^{72} - 10q^{73} - 15q^{74} + 19q^{75} - 15q^{77} + 48q^{78} - 10q^{79} + 108q^{80} + 59q^{81} - 10q^{82} - 30q^{83} - 100q^{84} - 10q^{85} - 33q^{86} + 8q^{88} + 30q^{89} - 180q^{90} + 16q^{91} + 72q^{92} - 2q^{93} - 10q^{94} + 45q^{96} - 6q^{97} - 10q^{99} + O(q^{100}) \)

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.cb.a \(736\) \(5.534\) None \(0\) \(-3\) \(-9\) \(-5\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database