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Properties

Label 3721.2.o
Level $3721$
Weight $2$
Character orbit 3721.o
Rep. character $\chi_{3721}(13,\cdot)$
Character field $\Q(\zeta_{183})$
Dimension $37680$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.o (of order \(183\) and degree \(120\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3721 \)
Character field: \(\Q(\zeta_{183})\)
Sturm bound: \(630\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3721, [\chi])\).

Total New Old
Modular forms 37920 37920 0
Cusp forms 37680 37680 0
Eisenstein series 240 240 0

Trace form

\( 37680 q - 122 q^{2} - 116 q^{3} + 188 q^{4} - 120 q^{5} - 121 q^{6} - 121 q^{7} - 116 q^{8} - 744 q^{9} + O(q^{10}) \) \( 37680 q - 122 q^{2} - 116 q^{3} + 188 q^{4} - 120 q^{5} - 121 q^{6} - 121 q^{7} - 116 q^{8} - 744 q^{9} - 122 q^{10} - 120 q^{11} - 115 q^{12} - 127 q^{13} - 370 q^{14} - 130 q^{15} + 184 q^{16} - 126 q^{17} - 112 q^{18} - 123 q^{19} - 136 q^{20} - 120 q^{21} - 121 q^{22} - 114 q^{23} - 132 q^{24} + 196 q^{25} - 131 q^{26} - 92 q^{27} - 118 q^{28} - 106 q^{29} - 128 q^{30} - 133 q^{31} - 118 q^{32} - 132 q^{33} - 94 q^{34} - 135 q^{35} + 173 q^{36} - 126 q^{37} - 146 q^{38} - 130 q^{39} - 137 q^{40} - 126 q^{41} + 552 q^{42} - 10 q^{43} + 136 q^{44} - 827 q^{45} + 192 q^{46} - 122 q^{47} - 126 q^{48} + 169 q^{49} - 108 q^{50} - 106 q^{51} - 130 q^{52} - 160 q^{53} - 148 q^{54} - 102 q^{55} - 114 q^{56} + 378 q^{57} - 80 q^{58} + 121 q^{59} - 142 q^{60} - 376 q^{61} - 148 q^{62} - 140 q^{63} - 716 q^{64} - 112 q^{65} + 378 q^{66} - 105 q^{67} - 95 q^{68} - 84 q^{69} - 130 q^{70} - 119 q^{71} + 709 q^{72} - 98 q^{73} - 142 q^{74} - 151 q^{75} - 129 q^{76} - 859 q^{77} - 135 q^{78} - 106 q^{79} - 1480 q^{80} - 814 q^{81} + 421 q^{82} - 138 q^{83} - 112 q^{84} - 1366 q^{85} - 92 q^{86} + 343 q^{87} - 118 q^{88} - 130 q^{89} - 1317 q^{90} - 122 q^{91} - 155 q^{92} - 130 q^{93} - 196 q^{94} + 204 q^{95} + 96 q^{96} - 129 q^{97} - 120 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3721, [\chi])\) into newform subspaces

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