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Properties

Label 3721.2.c
Level $3721$
Weight $2$
Character orbit 3721.c
Rep. character $\chi_{3721}(1660,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $552$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 692 668 24
Cusp forms 568 552 16
Eisenstein series 124 116 8

Trace form

\( 552 q + 6 q^{3} - 250 q^{4} + 2 q^{5} + q^{6} + q^{7} + 6 q^{8} + 438 q^{9} + O(q^{10}) \) \( 552 q + 6 q^{3} - 250 q^{4} + 2 q^{5} + q^{6} + q^{7} + 6 q^{8} + 438 q^{9} + 2 q^{11} + 7 q^{12} - 5 q^{13} - 4 q^{14} - 8 q^{15} - 194 q^{16} - 4 q^{17} + 10 q^{18} - q^{19} - 14 q^{20} + 2 q^{21} + q^{22} + 8 q^{23} - 10 q^{24} - 152 q^{25} - 9 q^{26} + 30 q^{27} + 4 q^{28} + 16 q^{29} - 6 q^{30} - 11 q^{31} + 4 q^{32} - 10 q^{33} + 28 q^{34} - 13 q^{35} - 145 q^{36} - 4 q^{37} - 24 q^{38} - 8 q^{39} - 15 q^{40} - 4 q^{41} + 3 q^{42} - 10 q^{43} + 14 q^{44} + 27 q^{45} - 7 q^{46} - 20 q^{48} - 119 q^{49} + 14 q^{50} + 16 q^{51} + 24 q^{52} - 38 q^{53} - 26 q^{54} + 20 q^{55} + 8 q^{56} + 12 q^{57} + 74 q^{58} - q^{59} - 20 q^{60} - 122 q^{62} - 18 q^{63} + 166 q^{64} - 2 q^{65} - 4 q^{66} + 17 q^{67} + 27 q^{68} + 38 q^{69} + 16 q^{70} + 3 q^{71} + 38 q^{72} + 24 q^{73} - 20 q^{74} - 29 q^{75} - 23 q^{76} - 17 q^{77} - 13 q^{78} + 16 q^{79} - 16 q^{80} + 8 q^{81} - 6 q^{82} - 16 q^{83} + 10 q^{84} - 24 q^{85} + 18 q^{86} - 23 q^{87} + 36 q^{88} - 8 q^{89} + 25 q^{90} - 33 q^{92} - 8 q^{93} - 74 q^{94} + 82 q^{95} - 26 q^{96} - 19 q^{97} + 2 q^{98} - 6 q^{99} + O(q^{100}) \)

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

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