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Properties

Label 3721.2.k
Level $3721$
Weight $2$
Character orbit 3721.k
Rep. character $\chi_{3721}(432,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2200$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.k (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 2776 2664 112
Cusp forms 2280 2200 80
Eisenstein series 496 464 32

Trace form

\( 2200 q + 7 q^{2} + 4 q^{3} - 231 q^{4} + 18 q^{5} - 15 q^{6} + 11 q^{7} + 10 q^{8} - 416 q^{9} + O(q^{10}) \) \( 2200 q + 7 q^{2} + 4 q^{3} - 231 q^{4} + 18 q^{5} - 15 q^{6} + 11 q^{7} + 10 q^{8} - 416 q^{9} + 13 q^{10} - 41 q^{12} + 14 q^{13} - 15 q^{14} - 10 q^{15} + 205 q^{16} - 6 q^{17} - 46 q^{18} + 35 q^{19} + 14 q^{20} + 33 q^{21} + 19 q^{22} - 30 q^{23} - 5 q^{24} + 157 q^{25} + 4 q^{26} - 11 q^{27} - 33 q^{29} - 21 q^{31} + 54 q^{32} - 5 q^{33} - 38 q^{34} - 14 q^{35} - 74 q^{36} + 10 q^{37} - 21 q^{39} - 93 q^{40} - 3 q^{41} + 75 q^{42} - 4 q^{43} - 107 q^{44} - 39 q^{45} - 95 q^{46} + 60 q^{47} + 25 q^{48} - 108 q^{49} + 47 q^{51} + 13 q^{52} + 10 q^{53} + 55 q^{54} + 32 q^{55} - 10 q^{56} - 74 q^{57} + 42 q^{58} + 41 q^{59} + 200 q^{60} - 350 q^{62} - 42 q^{63} + 200 q^{64} + 89 q^{65} - 16 q^{66} - 31 q^{67} + 26 q^{68} + 30 q^{69} - 44 q^{70} - 23 q^{71} - 19 q^{73} + 48 q^{74} - 9 q^{75} + 37 q^{76} - 3 q^{77} - 85 q^{78} - 61 q^{79} - 73 q^{80} - 94 q^{81} + 66 q^{82} + 7 q^{83} - 190 q^{84} + 10 q^{85} - 52 q^{86} + 61 q^{87} + 22 q^{88} + 15 q^{89} - 153 q^{90} - 72 q^{91} - 59 q^{92} + 3 q^{93} - 10 q^{94} - 3 q^{95} - 100 q^{96} + 36 q^{97} + 25 q^{98} - 125 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3721, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3721, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 2}\)