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Properties

Label 3721.2.n
Level $3721$
Weight $2$
Character orbit 3721.n
Rep. character $\chi_{3721}(60,\cdot)$
Character field $\Q(\zeta_{122})$
Dimension $18840$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.n (of order \(122\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3721 \)
Character field: \(\Q(\zeta_{122})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 18960 18960 0
Cusp forms 18840 18840 0
Eisenstein series 120 120 0

Trace form

\( 18840 q - 61 q^{2} - 57 q^{3} + 257 q^{4} - 61 q^{5} - 61 q^{6} - 61 q^{7} - 61 q^{8} - 375 q^{9} + O(q^{10}) \) \( 18840 q - 61 q^{2} - 57 q^{3} + 257 q^{4} - 61 q^{5} - 61 q^{6} - 61 q^{7} - 61 q^{8} - 375 q^{9} - 61 q^{10} - 61 q^{11} - 81 q^{12} - 73 q^{13} + 73 q^{14} - 49 q^{15} - 367 q^{16} - 61 q^{17} - 61 q^{18} - 73 q^{19} - 49 q^{20} - 61 q^{21} - 77 q^{22} - 61 q^{23} - 61 q^{24} - 363 q^{25} - 61 q^{26} - 45 q^{27} - 61 q^{28} - 61 q^{29} - 61 q^{30} - 61 q^{31} - 61 q^{32} - 61 q^{33} - 65 q^{34} - 61 q^{35} + 281 q^{36} - 61 q^{37} - 61 q^{38} - 49 q^{39} - 61 q^{40} - 49 q^{41} + 550 q^{42} + 61 q^{43} + 183 q^{44} + 281 q^{45} + 244 q^{46} - 85 q^{47} - 33 q^{48} + 269 q^{49} - 61 q^{50} - 61 q^{51} - 29 q^{52} - 61 q^{53} - 61 q^{54} - 61 q^{55} - 109 q^{56} - 525 q^{57} - 65 q^{58} - 305 q^{59} - 97 q^{60} + 53 q^{61} - 31 q^{62} - 61 q^{63} + 241 q^{64} - 55 q^{65} - 513 q^{66} - 61 q^{67} - 61 q^{68} - 61 q^{69} - 19 q^{70} - 61 q^{71} + 732 q^{72} - 77 q^{73} - 97 q^{74} - 69 q^{75} - 33 q^{76} + 287 q^{77} - 61 q^{78} - 61 q^{79} + 586 q^{80} - 375 q^{81} - 549 q^{82} - 85 q^{83} - 61 q^{84} - 671 q^{85} - 7 q^{86} - 549 q^{87} - 41 q^{88} - 61 q^{89} + 549 q^{90} - 61 q^{91} - 61 q^{92} - 61 q^{93} - 61 q^{94} - 317 q^{95} + 183 q^{96} - 55 q^{97} - 61 q^{98} - 61 q^{99} + O(q^{100}) \)

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.