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Properties

Label 1441.2.bg
Level $1441$
Weight $2$
Character orbit 1441.bg
Rep. character $\chi_{1441}(36,\cdot)$
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.bg (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

\( 6240 q - 25 q^{2} - 32 q^{3} - 545 q^{4} - 42 q^{5} - 34 q^{6} - 25 q^{7} + 3 q^{8} + 106 q^{9} + O(q^{10}) \) \( 6240 q - 25 q^{2} - 32 q^{3} - 545 q^{4} - 42 q^{5} - 34 q^{6} - 25 q^{7} + 3 q^{8} + 106 q^{9} - 98 q^{10} - 52 q^{11} - 177 q^{12} - 46 q^{13} - 24 q^{14} - 46 q^{15} - 517 q^{16} - 164 q^{17} - 14 q^{18} - 49 q^{19} - 238 q^{20} - 108 q^{21} - 40 q^{22} + 50 q^{23} - 59 q^{24} + 58 q^{25} - 343 q^{26} - 68 q^{27} + 34 q^{28} - 50 q^{29} - 102 q^{30} - 26 q^{31} - 36 q^{32} + 25 q^{33} - 108 q^{34} - 43 q^{35} + 86 q^{36} - 50 q^{37} - 33 q^{38} - 36 q^{39} + 77 q^{40} + 26 q^{41} - 94 q^{42} - 10 q^{43} + 141 q^{44} - 179 q^{45} - 40 q^{46} - 37 q^{47} + 59 q^{48} + 123 q^{49} - 40 q^{50} - 20 q^{51} - 53 q^{52} + 68 q^{53} + 69 q^{54} - 285 q^{55} - 59 q^{56} - 59 q^{57} - 12 q^{58} - 93 q^{59} - 321 q^{60} - 23 q^{61} + 69 q^{62} - 52 q^{63} - 473 q^{64} - 79 q^{65} - 46 q^{66} - 79 q^{67} + 44 q^{68} + 266 q^{69} - 163 q^{70} - 53 q^{71} + 324 q^{72} - 492 q^{73} + 115 q^{74} - 67 q^{75} - 37 q^{76} - 33 q^{77} - 49 q^{78} + 187 q^{79} - 343 q^{80} + 82 q^{81} - 31 q^{82} - 67 q^{83} - 68 q^{84} - 162 q^{85} - 69 q^{86} - 114 q^{87} + 54 q^{88} - 281 q^{89} - 373 q^{90} - 30 q^{91} + 82 q^{92} - 85 q^{93} + 272 q^{94} - 97 q^{95} + 49 q^{96} + 211 q^{97} - 275 q^{98} + 197 q^{99} + O(q^{100}) \)

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.