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Properties

Label 1716.2.dm
Level $1716$
Weight $2$
Character orbit 1716.dm
Rep. character $\chi_{1716}(167,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5248$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1716.dm (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1716 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1716, [\chi])\).

Total New Old
Modular forms 5504 5504 0
Cusp forms 5248 5248 0
Eisenstein series 256 256 0

Trace form

\( 5248 q - 36 q^{4} - 20 q^{6} - 12 q^{9} + O(q^{10}) \) \( 5248 q - 36 q^{4} - 20 q^{6} - 12 q^{9} - 80 q^{13} - 36 q^{16} - 20 q^{18} - 8 q^{22} - 20 q^{24} - 40 q^{28} - 30 q^{30} - 44 q^{33} - 24 q^{34} - 18 q^{36} - 48 q^{37} - 80 q^{40} + 26 q^{42} - 24 q^{45} - 80 q^{46} - 2 q^{48} - 72 q^{49} - 40 q^{52} - 40 q^{57} - 112 q^{58} - 100 q^{60} - 40 q^{61} + 188 q^{66} - 36 q^{69} - 124 q^{70} - 20 q^{72} - 80 q^{73} - 44 q^{78} - 12 q^{81} - 216 q^{82} - 120 q^{84} - 80 q^{85} - 48 q^{88} - 64 q^{93} - 20 q^{94} - 50 q^{96} - 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1716, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.