Properties

Label 1716.2.dc
Level $1716$
Weight $2$
Character orbit 1716.dc
Rep. character $\chi_{1716}(191,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2624$
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.dc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1716 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2752 2752 0
Cusp forms 2624 2624 0
Eisenstein series 128 128 0

Trace form

\( 2624 q - 6 q^{4} - 11 q^{6} - 6 q^{9} + O(q^{10}) \) \( 2624 q - 6 q^{4} - 11 q^{6} - 6 q^{9} - 32 q^{10} - 20 q^{12} - 24 q^{13} + 6 q^{16} - 4 q^{18} - 40 q^{21} - 36 q^{22} + 19 q^{24} + 544 q^{25} + 38 q^{28} - 23 q^{30} - 20 q^{33} - 24 q^{34} - 5 q^{36} - 12 q^{37} - 120 q^{40} + 23 q^{42} - 36 q^{45} - 14 q^{46} + 19 q^{48} - 292 q^{49} + 16 q^{52} - 132 q^{54} + 46 q^{58} + 52 q^{60} - 12 q^{61} - 96 q^{64} - 154 q^{66} + 46 q^{69} - 252 q^{70} - 45 q^{72} - 48 q^{73} + 60 q^{76} - 64 q^{78} - 6 q^{81} + 28 q^{82} + 18 q^{84} - 52 q^{85} - 78 q^{88} - 10 q^{90} - 34 q^{93} + 46 q^{94} - 14 q^{96} - 12 q^{97} + O(q^{100}) \)

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

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