Properties

Label 121.2.e
Level 121
Weight 2
Character orbit e
Rep. character \(\chi_{121}(12,\cdot)\)
Character field \(\Q(\zeta_{11})\)
Dimension 100
Newform subspaces 1
Sturm bound 22
Trace bound 0

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 121.e (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(121, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 100 100 0
Eisenstein series 20 20 0

Trace form

\( 100q - 6q^{2} - 18q^{3} - 16q^{4} - 7q^{5} - 23q^{6} - q^{7} + 4q^{8} + 70q^{9} + O(q^{10}) \) \( 100q - 6q^{2} - 18q^{3} - 16q^{4} - 7q^{5} - 23q^{6} - q^{7} + 4q^{8} + 70q^{9} - 13q^{10} - 12q^{11} - 51q^{12} - 34q^{13} - 17q^{14} - 46q^{15} + 10q^{16} + 9q^{17} - 31q^{18} + 9q^{19} + 21q^{20} - 14q^{21} - 20q^{22} - 11q^{23} - 72q^{24} + 11q^{25} + 33q^{26} - 60q^{27} + 49q^{28} + 19q^{29} + 26q^{30} - 13q^{31} + 44q^{32} + q^{33} + 31q^{34} + 39q^{35} - 17q^{36} - 16q^{37} - 29q^{38} + 16q^{39} + 2q^{40} + 39q^{41} + 42q^{42} + 39q^{43} + 53q^{44} - 33q^{45} + 59q^{46} + 21q^{47} + 56q^{48} - 11q^{49} - 58q^{50} - 139q^{51} - 75q^{52} - 73q^{53} - 156q^{54} - 34q^{55} + 10q^{56} - 41q^{57} - 38q^{58} + 33q^{59} + 100q^{60} + 39q^{61} + 44q^{62} - 76q^{63} - 16q^{64} + 36q^{65} + 75q^{66} - 4q^{67} + 119q^{68} + 32q^{69} + 61q^{70} + 5q^{71} + 63q^{72} + 37q^{73} + 109q^{74} + 58q^{75} - 91q^{76} - 53q^{77} - 24q^{78} - 9q^{79} - 36q^{80} + 28q^{81} + 33q^{82} + 79q^{83} + 176q^{84} - 11q^{85} + 85q^{86} + 76q^{87} + 33q^{88} - 48q^{89} - 89q^{90} - 14q^{91} - 113q^{92} + 31q^{93} - 38q^{94} + 21q^{95} + 84q^{96} + 40q^{97} - 22q^{98} - 53q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
121.2.e.a \(100\) \(0.966\) None \(-6\) \(-18\) \(-7\) \(-1\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database