Properties

Label 268.2.j
Level 268
Weight 2
Character orbit j
Rep. character \(\chi_{268}(3,\cdot)\)
Character field \(\Q(\zeta_{22})\)
Dimension 320
Newform subspaces 1
Sturm bound 68
Trace bound 0

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Defining parameters

Level: \( N \) = \( 268 = 2^{2} \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 268.j (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 268 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(68\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(268, [\chi])\).

Total New Old
Modular forms 360 360 0
Cusp forms 320 320 0
Eisenstein series 40 40 0

Trace form

\( 320q - 11q^{2} - 7q^{4} - 22q^{5} - 5q^{6} - 44q^{8} - 50q^{9} + O(q^{10}) \) \( 320q - 11q^{2} - 7q^{4} - 22q^{5} - 5q^{6} - 44q^{8} - 50q^{9} + 14q^{10} - 11q^{12} - 22q^{13} - 9q^{14} + q^{16} - 36q^{17} - 11q^{18} - 11q^{20} + 38q^{21} + 40q^{22} - 31q^{24} + 6q^{25} - 19q^{26} - 66q^{28} - 64q^{29} + 44q^{32} + 10q^{33} - 11q^{34} - 36q^{36} - 32q^{37} + 10q^{40} - 22q^{41} - 11q^{42} - 11q^{44} + 110q^{45} + 44q^{46} - 11q^{48} - 14q^{49} - 121q^{50} - 11q^{52} - 22q^{53} - 88q^{54} + 19q^{56} - 154q^{57} - 33q^{58} + 31q^{60} - 22q^{61} - 37q^{62} + 2q^{64} - 38q^{65} + 170q^{68} - 22q^{69} - 11q^{70} - 121q^{72} - 114q^{73} - 33q^{74} - 73q^{76} + 2q^{77} - 11q^{78} - 11q^{80} - 54q^{81} - 121q^{82} + 23q^{84} - 22q^{85} - q^{86} - 17q^{88} - 54q^{89} + 91q^{90} - 63q^{92} + 94q^{93} - 11q^{94} + 148q^{96} - 11q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(268, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
268.2.j.a \(320\) \(2.140\) None \(-11\) \(0\) \(-22\) \(0\)