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Properties

Label 3680.2.dt
Level $3680$
Weight $2$
Character orbit 3680.dt
Rep. character $\chi_{3680}(37,\cdot)$
Character field $\Q(\zeta_{88})$
Dimension $22880$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3680 = 2^{5} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3680.dt (of order \(88\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3680 \)
Character field: \(\Q(\zeta_{88})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3680, [\chi])\).

Total New Old
Modular forms 23200 23200 0
Cusp forms 22880 22880 0
Eisenstein series 320 320 0

Trace form

\( 22880 q - 36 q^{2} - 36 q^{3} - 44 q^{5} - 72 q^{6} - 36 q^{8} + O(q^{10}) \) \( 22880 q - 36 q^{2} - 36 q^{3} - 44 q^{5} - 72 q^{6} - 36 q^{8} - 44 q^{10} - 88 q^{11} - 36 q^{12} - 36 q^{13} - 72 q^{16} - 20 q^{18} - 44 q^{20} - 88 q^{21} - 36 q^{25} - 72 q^{26} - 60 q^{27} - 44 q^{28} - 44 q^{30} - 144 q^{31} + 4 q^{32} - 88 q^{33} + 88 q^{34} + 4 q^{35} - 72 q^{36} - 44 q^{37} - 44 q^{38} - 44 q^{40} - 72 q^{41} + 396 q^{42} - 44 q^{43} - 80 q^{46} - 204 q^{48} - 2192 q^{49} - 52 q^{50} - 88 q^{51} + 36 q^{52} - 44 q^{53} - 36 q^{55} - 88 q^{56} + 28 q^{58} - 44 q^{60} - 88 q^{61} - 92 q^{62} - 88 q^{63} + 96 q^{64} - 88 q^{65} - 88 q^{66} - 44 q^{67} - 24 q^{69} - 96 q^{70} - 72 q^{71} - 100 q^{72} - 12 q^{75} - 88 q^{76} + 20 q^{77} - 52 q^{78} - 44 q^{80} + 140 q^{82} - 44 q^{83} - 36 q^{85} - 88 q^{86} - 72 q^{87} - 44 q^{88} - 44 q^{90} - 16 q^{92} - 56 q^{93} - 64 q^{94} - 72 q^{95} - 72 q^{96} - 88 q^{97} + 36 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3680, [\chi])\) into newform subspaces

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