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Properties

Label 1441.2.by
Level $1441$
Weight $2$
Character orbit 1441.by
Rep. character $\chi_{1441}(2,\cdot)$
Character field $\Q(\zeta_{130})$
Dimension $6240$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.by (of order \(130\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1441 \)
Character field: \(\Q(\zeta_{130})\)
Sturm bound: \(264\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1441, [\chi])\).

Total New Old
Modular forms 6432 6432 0
Cusp forms 6240 6240 0
Eisenstein series 192 192 0

Trace form

\( 6240 q - 60 q^{2} - 34 q^{3} + 90 q^{4} - 39 q^{5} - 75 q^{6} - 85 q^{7} - 70 q^{8} + 76 q^{9} + O(q^{10}) \) \( 6240 q - 60 q^{2} - 34 q^{3} + 90 q^{4} - 39 q^{5} - 75 q^{6} - 85 q^{7} - 70 q^{8} + 76 q^{9} + 10 q^{10} - 49 q^{11} - 174 q^{12} - 50 q^{13} - 34 q^{14} - 35 q^{15} + 88 q^{16} - 220 q^{17} - 70 q^{18} - 50 q^{19} + 79 q^{20} + 20 q^{21} - 47 q^{22} + 16 q^{23} - 75 q^{24} + 83 q^{25} - 351 q^{26} - 67 q^{27} - 65 q^{28} - 60 q^{29} - 130 q^{30} - 24 q^{31} + 100 q^{32} - 315 q^{33} - 98 q^{34} - 65 q^{35} - 569 q^{36} - 19 q^{37} - 40 q^{38} - 50 q^{39} - 105 q^{40} - 65 q^{41} + 180 q^{43} + 409 q^{44} - 196 q^{45} - 70 q^{46} - 54 q^{47} - 60 q^{48} - 103 q^{49} - 75 q^{50} - 15 q^{51} - 175 q^{52} + 170 q^{53} + 225 q^{54} - 195 q^{55} - 139 q^{56} - 75 q^{57} + 12 q^{58} - 37 q^{59} - 228 q^{60} - 55 q^{62} - 115 q^{63} + 102 q^{64} + 65 q^{65} + 13 q^{66} - 69 q^{67} + 160 q^{68} + 248 q^{69} - 105 q^{70} - 9 q^{71} - 105 q^{72} - 70 q^{73} - 25 q^{74} - 157 q^{75} + 205 q^{76} - 44 q^{77} - 135 q^{78} - 105 q^{79} - 225 q^{80} + 121 q^{81} + 31 q^{82} - 75 q^{83} - 195 q^{84} - 55 q^{85} + 66 q^{86} + 75 q^{87} - 82 q^{88} + 101 q^{89} + 385 q^{90} + 29 q^{91} - 34 q^{92} - 4 q^{93} - 60 q^{94} - 80 q^{95} - 45 q^{96} - 273 q^{97} - 15 q^{98} + 74 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1441, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.