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Properties

Label 3721.2.b
Level $3721$
Weight $2$
Character orbit 3721.b
Rep. character $\chi_{3721}(3720,\cdot)$
Character field $\Q$
Dimension $276$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 346 334 12
Cusp forms 284 276 8
Eisenstein series 62 58 4

Trace form

\( 276 q + 4 q^{3} - 242 q^{4} + 216 q^{9} + O(q^{10}) \) \( 276 q + 4 q^{3} - 242 q^{4} + 216 q^{9} - 20 q^{12} - 12 q^{13} + 12 q^{14} + 12 q^{15} + 194 q^{16} - 12 q^{19} + 12 q^{20} - 16 q^{22} + 168 q^{25} + 16 q^{27} - 4 q^{34} - 98 q^{36} + 12 q^{39} + 12 q^{41} - 60 q^{42} - 24 q^{45} - 16 q^{46} - 24 q^{47} + 12 q^{48} - 80 q^{49} + 16 q^{52} - 48 q^{56} + 24 q^{57} + 12 q^{58} - 36 q^{60} - 18 q^{62} - 78 q^{64} - 6 q^{65} + 20 q^{66} + 54 q^{70} - 16 q^{73} - 36 q^{74} - 8 q^{75} + 44 q^{76} - 6 q^{77} - 24 q^{80} + 36 q^{81} - 24 q^{83} + 66 q^{86} + 4 q^{88} - 12 q^{95} - 6 q^{97} + O(q^{100}) \)

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

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