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Properties

Label 3721.2.g
Level $3721$
Weight $2$
Character orbit 3721.g
Rep. character $\chi_{3721}(601,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1104$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.g (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 1384 1336 48
Cusp forms 1136 1104 32
Eisenstein series 248 232 16

Trace form

\( 1104 q + 5 q^{2} + q^{3} + 247 q^{4} + 15 q^{6} - 10 q^{7} + 5 q^{8} - 221 q^{9} + O(q^{10}) \) \( 1104 q + 5 q^{2} + q^{3} + 247 q^{4} + 15 q^{6} - 10 q^{7} + 5 q^{8} - 221 q^{9} + 5 q^{10} + 12 q^{13} + 18 q^{14} + 13 q^{15} - 209 q^{16} + 10 q^{18} - 3 q^{19} + 13 q^{20} - 19 q^{22} + 15 q^{23} - 10 q^{24} - 158 q^{25} - 10 q^{26} + 4 q^{27} - 35 q^{28} - 45 q^{30} + 15 q^{31} - 25 q^{33} + 14 q^{34} - 10 q^{35} + 93 q^{36} + 5 q^{37} + 15 q^{38} + 3 q^{39} - 12 q^{41} + 15 q^{42} + 25 q^{43} + 50 q^{44} - 36 q^{45} - 19 q^{46} - 6 q^{47} - 12 q^{48} + 130 q^{49} - 50 q^{51} + 54 q^{52} + 20 q^{53} + 20 q^{54} - 20 q^{55} + 28 q^{56} + 11 q^{57} + 33 q^{58} - 5 q^{59} - 14 q^{60} - 232 q^{62} + 5 q^{63} + 53 q^{64} - 14 q^{65} - 5 q^{66} + 55 q^{67} - 80 q^{68} + 15 q^{69} + 11 q^{70} + 50 q^{71} + 11 q^{73} - 24 q^{74} + 88 q^{75} + 11 q^{76} - 69 q^{77} - 50 q^{78} - 40 q^{79} + 49 q^{80} - 21 q^{81} - 31 q^{83} + 25 q^{84} - 55 q^{85} - 41 q^{86} - 25 q^{87} - 19 q^{88} - 60 q^{89} + 15 q^{91} + 5 q^{92} - 65 q^{94} - 48 q^{95} + 25 q^{96} - 39 q^{97} - 10 q^{98} + 5 q^{99} + O(q^{100}) \)

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

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