Properties

Label 668.2.h
Level $668$
Weight $2$
Character orbit 668.h
Rep. character $\chi_{668}(15,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $6724$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.h (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 668 \)
Character field: \(\Q(\zeta_{166})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(668, [\chi])\).

Total New Old
Modular forms 7052 7052 0
Cusp forms 6724 6724 0
Eisenstein series 328 328 0

Trace form

\( 6724q - 81q^{2} - 85q^{4} - 166q^{5} - 75q^{6} - 75q^{8} - 84q^{9} + O(q^{10}) \) \( 6724q - 81q^{2} - 85q^{4} - 166q^{5} - 75q^{6} - 75q^{8} - 84q^{9} - 83q^{10} - 101q^{12} - 166q^{13} - 93q^{14} - 93q^{16} - 166q^{17} - 63q^{18} - 83q^{20} - 166q^{21} - 103q^{22} - 93q^{24} - 88q^{25} - 83q^{26} - 83q^{28} - 170q^{29} - 83q^{30} - 101q^{32} - 174q^{33} - 83q^{34} - 113q^{36} - 166q^{37} - 47q^{38} - 83q^{40} - 166q^{41} - 86q^{42} - 78q^{44} - 166q^{45} - 83q^{46} - 110q^{48} - 84q^{49} - 43q^{50} - 83q^{52} - 166q^{53} - 86q^{54} - 133q^{56} - 174q^{57} - 61q^{58} - 83q^{60} - 202q^{61} - 88q^{62} - 91q^{64} - 190q^{65} - 107q^{66} - 83q^{68} - 166q^{69} - 83q^{70} - 52q^{72} - 166q^{73} - 83q^{74} - 47q^{76} - 166q^{77} - 83q^{78} - 83q^{80} - 280q^{81} - 83q^{82} - 116q^{84} - 150q^{85} - 83q^{86} - 63q^{88} - 194q^{89} - 83q^{90} - 83q^{92} - 238q^{93} - 173q^{94} - 85q^{96} - 162q^{97} - 134q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(668, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
668.2.h.a \(6724\) \(5.334\) None \(-81\) \(0\) \(-166\) \(0\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database