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Properties

Label 3920.2.dt
Level $3920$
Weight $2$
Character orbit 3920.dt
Rep. character $\chi_{3920}(13,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $8016$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3920.dt (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3920 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3920, [\chi])\).

Total New Old
Modular forms 8112 8112 0
Cusp forms 8016 8016 0
Eisenstein series 96 96 0

Trace form

\( 8016 q - 10 q^{2} - 14 q^{5} - 28 q^{6} - 22 q^{8} - 1320 q^{9} + O(q^{10}) \) \( 8016 q - 10 q^{2} - 14 q^{5} - 28 q^{6} - 22 q^{8} - 1320 q^{9} - 14 q^{10} - 20 q^{11} - 14 q^{12} - 20 q^{15} - 20 q^{16} - 28 q^{17} - 4 q^{18} - 14 q^{20} - 24 q^{21} - 18 q^{22} - 28 q^{26} - 26 q^{28} - 44 q^{30} - 10 q^{32} - 28 q^{33} - 56 q^{34} - 14 q^{35} + 12 q^{36} + 14 q^{38} + 48 q^{39} - 14 q^{40} + 22 q^{42} - 20 q^{43} - 14 q^{45} - 20 q^{46} - 28 q^{47} - 24 q^{50} - 20 q^{51} - 14 q^{52} - 20 q^{53} + 84 q^{54} - 24 q^{56} - 60 q^{57} + 30 q^{58} + 6 q^{60} - 28 q^{61} + 14 q^{62} + 4 q^{63} - 20 q^{65} - 28 q^{66} - 94 q^{70} + 184 q^{72} + 40 q^{74} - 14 q^{75} - 28 q^{76} - 52 q^{77} + 110 q^{78} - 1312 q^{81} + 126 q^{82} - 48 q^{84} + 10 q^{85} - 36 q^{86} + 132 q^{88} - 308 q^{90} - 8 q^{91} + 42 q^{92} + 28 q^{95} + 224 q^{96} + 172 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

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