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Properties

Label 3721.2.i
Level $3721$
Weight $2$
Character orbit 3721.i
Rep. character $\chi_{3721}(574,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2208$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.i (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 2768 2672 96
Cusp forms 2272 2208 64
Eisenstein series 496 464 32

Trace form

\( 2208 q + 10 q^{2} + 4 q^{3} + 260 q^{4} - 2 q^{5} - q^{6} - q^{7} + 4 q^{8} - 438 q^{9} + O(q^{10}) \) \( 2208 q + 10 q^{2} + 4 q^{3} + 260 q^{4} - 2 q^{5} - q^{6} - q^{7} + 4 q^{8} - 438 q^{9} - 15 q^{10} + 18 q^{11} + 53 q^{12} - 11 q^{14} - 2 q^{15} + 184 q^{16} + 24 q^{17} + 15 q^{18} - 9 q^{19} + 4 q^{20} + 3 q^{21} - q^{22} + 2 q^{23} - 15 q^{24} + 132 q^{25} - 16 q^{26} - 35 q^{27} - 4 q^{28} + 4 q^{29} - 54 q^{30} + 11 q^{31} - 34 q^{32} + 35 q^{33} - 18 q^{34} + 58 q^{35} + 65 q^{36} + 14 q^{37} + 24 q^{38} - 17 q^{39} + 60 q^{40} - 11 q^{41} - 73 q^{42} - 40 q^{43} - 29 q^{44} - 12 q^{45} + 97 q^{46} - 40 q^{47} - 75 q^{48} + 99 q^{49} + 56 q^{50} + 9 q^{51} + 51 q^{52} - 17 q^{53} + q^{54} + 60 q^{55} + 102 q^{56} + 38 q^{57} - 89 q^{58} + 11 q^{59} + 20 q^{60} - 358 q^{62} + 58 q^{63} - 146 q^{64} - 53 q^{65} - 26 q^{66} + 13 q^{67} + 3 q^{68} + 32 q^{69} - 56 q^{70} - 63 q^{71} - 18 q^{72} + 46 q^{73} + 10 q^{74} - q^{75} - 47 q^{76} + 37 q^{77} + 103 q^{78} + 49 q^{79} - 74 q^{80} - 128 q^{81} - 39 q^{82} - 39 q^{83} - 21 q^{85} - 68 q^{86} - 17 q^{87} - 86 q^{88} - 32 q^{89} + 60 q^{90} - 70 q^{91} - 77 q^{92} - 67 q^{93} + 64 q^{94} - 47 q^{95} + 16 q^{96} - 31 q^{97} - 127 q^{98} + 31 q^{99} + O(q^{100}) \)

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

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