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Properties

Label 3721.2.m
Level $3721$
Weight $2$
Character orbit 3721.m
Rep. character $\chi_{3721}(62,\cdot)$
Character field $\Q(\zeta_{61})$
Dimension $18780$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.m (of order \(61\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3721 \)
Character field: \(\Q(\zeta_{61})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 18900 18900 0
Cusp forms 18780 18780 0
Eisenstein series 120 120 0

Trace form

\( 18780 q - 58 q^{2} - 57 q^{3} - 364 q^{4} - 51 q^{5} - 47 q^{6} - 51 q^{7} - 52 q^{8} - 362 q^{9} + O(q^{10}) \) \( 18780 q - 58 q^{2} - 57 q^{3} - 364 q^{4} - 51 q^{5} - 47 q^{6} - 51 q^{7} - 52 q^{8} - 362 q^{9} - 37 q^{10} - 57 q^{11} - 25 q^{12} - 39 q^{13} - 155 q^{14} - 41 q^{15} - 336 q^{16} - 45 q^{17} - 26 q^{18} - 37 q^{19} - 23 q^{20} - 19 q^{21} - 41 q^{22} - 33 q^{23} + 9 q^{24} - 348 q^{25} - 19 q^{26} - 33 q^{27} - 9 q^{28} - 29 q^{29} + 17 q^{30} - 27 q^{31} + 10 q^{32} - 27 q^{33} - 11 q^{34} - 21 q^{35} - 268 q^{36} - 25 q^{37} - 19 q^{38} - 9 q^{39} + 29 q^{40} - 27 q^{41} - 636 q^{42} - 117 q^{43} - 235 q^{44} - 325 q^{45} - 306 q^{46} - 13 q^{47} + 43 q^{48} - 298 q^{49} + 48 q^{50} + 19 q^{51} + 45 q^{52} - 11 q^{53} + 43 q^{54} + 9 q^{55} + 51 q^{56} - 445 q^{57} + 5 q^{58} - 283 q^{59} + 91 q^{60} - 124 q^{61} + 61 q^{62} + 61 q^{63} - 240 q^{64} + 37 q^{65} - 381 q^{66} + 5 q^{67} + 71 q^{68} + 9 q^{69} + 73 q^{70} + 5 q^{71} - 649 q^{72} + 25 q^{73} + 49 q^{74} + 59 q^{75} + 35 q^{76} - 317 q^{77} + 81 q^{78} + 3 q^{79} - 530 q^{80} - 238 q^{81} - 472 q^{82} + 27 q^{83} + 141 q^{84} - 533 q^{85} + 53 q^{86} - 445 q^{87} + 115 q^{88} + 37 q^{89} - 447 q^{90} + 57 q^{91} + 101 q^{92} + 39 q^{93} + 67 q^{94} - 201 q^{95} - 87 q^{96} + 35 q^{97} + 108 q^{98} + 83 q^{99} + O(q^{100}) \)

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.