Properties

Label 693.2.ce
Level 693
Weight 2
Character orbit ce
Rep. character \(\chi_{693}(47,\cdot)\)
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.ce (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

\( 736q - 9q^{2} - 9q^{3} - 85q^{4} - 18q^{5} + 12q^{6} - 3q^{7} + 3q^{9} + O(q^{10}) \) \( 736q - 9q^{2} - 9q^{3} - 85q^{4} - 18q^{5} + 12q^{6} - 3q^{7} + 3q^{9} - 48q^{10} - 24q^{12} - 9q^{14} + 87q^{16} + 13q^{18} - 18q^{19} - 18q^{20} - 42q^{21} - 12q^{22} - 27q^{24} - 158q^{25} + 48q^{26} + 27q^{27} - 8q^{28} - 18q^{29} - 3q^{30} - 9q^{31} - 48q^{32} - 84q^{33} + 12q^{34} + 75q^{35} + 28q^{36} - 6q^{37} - 78q^{38} + 15q^{39} + 21q^{42} - 16q^{43} - 27q^{44} - 24q^{45} + 6q^{46} - 9q^{47} + 30q^{48} - 3q^{49} - 111q^{50} - 41q^{51} - 36q^{53} - 108q^{54} + 18q^{56} - 34q^{57} + 46q^{58} + 21q^{59} - 37q^{60} - 9q^{61} + 24q^{62} - 53q^{63} + 132q^{64} - 12q^{65} - 102q^{66} + 8q^{67} - 18q^{68} + 27q^{69} + 54q^{70} - 35q^{72} - 18q^{73} + 51q^{75} + 57q^{77} + 16q^{78} - 21q^{79} - 24q^{80} - 17q^{81} - 30q^{82} - 117q^{84} - 28q^{85} + 42q^{87} - 32q^{88} + 30q^{89} + 12q^{90} + 16q^{91} - 168q^{92} - 41q^{93} - 9q^{94} + 123q^{95} + 63q^{96} + 60q^{98} - 112q^{99} + O(q^{100}) \)

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.ce.a \(736\) \(5.534\) None \(-9\) \(-9\) \(-18\) \(-3\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database