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Properties

Label 1441.2.bi
Level $1441$
Weight $2$
Character orbit 1441.bi
Rep. character $\chi_{1441}(4,\cdot)$
Character field $\Q(\zeta_{65})$
Dimension $6240$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.bi (of order \(65\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1441 \)
Character field: \(\Q(\zeta_{65})\)
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

\( 6240 q - 40 q^{2} - 42 q^{3} + 90 q^{4} - 37 q^{5} - 9 q^{6} - 25 q^{7} - 42 q^{8} + 76 q^{9} + O(q^{10}) \) \( 6240 q - 40 q^{2} - 42 q^{3} + 90 q^{4} - 37 q^{5} - 9 q^{6} - 25 q^{7} - 42 q^{8} + 76 q^{9} - 108 q^{10} - 37 q^{11} - 42 q^{12} - 36 q^{13} - 54 q^{14} - 31 q^{15} + 88 q^{16} - 104 q^{17} - 34 q^{18} - 34 q^{19} + 87 q^{20} - 88 q^{21} - 85 q^{22} - 240 q^{23} - 69 q^{24} + 83 q^{25} - 283 q^{26} - 3 q^{27} - 61 q^{28} - 50 q^{29} - 22 q^{30} - 36 q^{31} + 4 q^{32} - 305 q^{33} - 118 q^{34} - 43 q^{35} - 569 q^{36} - 35 q^{37} - 28 q^{38} - 36 q^{39} + 107 q^{40} - 9 q^{41} + 16 q^{42} - 240 q^{43} - 399 q^{44} - 44 q^{45} - 60 q^{46} - 42 q^{47} + 24 q^{48} + 133 q^{49} - 5 q^{50} - 55 q^{51} + 47 q^{52} - 182 q^{53} - 231 q^{54} + 45 q^{55} - 129 q^{56} - 9 q^{57} - 52 q^{58} - 63 q^{59} + 124 q^{60} - 58 q^{61} + 99 q^{62} - 107 q^{63} + 102 q^{64} - 59 q^{65} - 41 q^{66} - 139 q^{67} - 206 q^{68} + 286 q^{69} + 547 q^{70} - 23 q^{71} + 259 q^{72} + 178 q^{73} + 95 q^{74} - 17 q^{75} - 297 q^{76} - 138 q^{77} - 89 q^{78} + 187 q^{79} + 147 q^{80} + 57 q^{81} - q^{82} - 97 q^{83} - 13 q^{84} + 213 q^{85} - 4 q^{86} - 119 q^{87} - 26 q^{88} + 49 q^{89} - 423 q^{90} - 55 q^{91} + 92 q^{92} + 182 q^{94} - 152 q^{95} - 51 q^{96} + 211 q^{97} + 5 q^{98} - 98 q^{99} + O(q^{100}) \)

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.