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Properties

Label 3800.2.dw
Level $3800$
Weight $2$
Character orbit 3800.dw
Rep. character $\chi_{3800}(429,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4768$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.dw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3800 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3800, [\chi])\).

Total New Old
Modular forms 4832 4832 0
Cusp forms 4768 4768 0
Eisenstein series 64 64 0

Trace form

\( 4768 q - 5 q^{2} - 3 q^{4} - 11 q^{6} - 50 q^{8} + 582 q^{9} + O(q^{10}) \) \( 4768 q - 5 q^{2} - 3 q^{4} - 11 q^{6} - 50 q^{8} + 582 q^{9} - 11 q^{10} - 20 q^{12} - 3 q^{14} - 20 q^{15} - 3 q^{16} - 10 q^{17} - 20 q^{20} + 45 q^{22} - 10 q^{23} - 16 q^{24} - 8 q^{25} - 20 q^{26} + 15 q^{28} - 36 q^{30} - 72 q^{31} - 10 q^{33} + 5 q^{34} - 13 q^{36} - 15 q^{38} - 48 q^{39} - 12 q^{40} - 6 q^{41} + 25 q^{42} + 31 q^{44} - 4 q^{46} - 10 q^{47} - 5 q^{48} - 4640 q^{49} + 22 q^{50} - 5 q^{52} - 32 q^{54} - 18 q^{55} + 72 q^{56} - 330 q^{58} + 48 q^{60} + 20 q^{62} + 60 q^{63} + 54 q^{64} - 52 q^{65} - 19 q^{66} - 12 q^{70} - 62 q^{71} - 110 q^{72} - 10 q^{73} - 18 q^{74} + 12 q^{76} + 10 q^{78} - 46 q^{79} + 29 q^{80} + 570 q^{81} + 76 q^{84} - 21 q^{86} - 40 q^{87} - 140 q^{88} - 6 q^{89} - 3 q^{90} + 45 q^{92} + 72 q^{94} - 178 q^{95} + 26 q^{96} - 10 q^{97} + 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3800, [\chi])\) into newform subspaces

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