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Properties

Label 3800.2.fa
Level $3800$
Weight $2$
Character orbit 3800.fa
Rep. character $\chi_{3800}(309,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $14304$
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.fa (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3800 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 14496 14496 0
Cusp forms 14304 14304 0
Eisenstein series 192 192 0

Trace form

\( 14304 q - 30 q^{2} - 18 q^{4} - 18 q^{6} - 15 q^{8} - 36 q^{9} + O(q^{10}) \) \( 14304 q - 30 q^{2} - 18 q^{4} - 18 q^{6} - 15 q^{8} - 36 q^{9} - 15 q^{10} - 15 q^{12} - 18 q^{14} - 48 q^{15} - 18 q^{16} - 60 q^{17} - 18 q^{20} - 30 q^{22} - 60 q^{23} - 24 q^{24} - 48 q^{25} - 24 q^{26} - 90 q^{28} - 33 q^{30} + 54 q^{31} - 60 q^{33} - 18 q^{34} - 36 q^{36} - 75 q^{38} - 72 q^{39} + 63 q^{40} - 36 q^{41} - 120 q^{42} + 6 q^{44} - 9 q^{46} - 60 q^{47} - 30 q^{48} + 6816 q^{49} - 21 q^{50} - 30 q^{52} - 84 q^{54} - 18 q^{55} - 162 q^{56} + 300 q^{58} - 105 q^{60} + 120 q^{62} - 270 q^{63} - 9 q^{64} - 24 q^{65} + 18 q^{66} - 72 q^{70} - 36 q^{71} - 480 q^{72} - 60 q^{73} + 18 q^{74} - 48 q^{76} - 75 q^{78} - 36 q^{79} - 75 q^{80} - 72 q^{81} - 135 q^{84} + 72 q^{86} - 30 q^{87} - 15 q^{88} - 36 q^{89} - 339 q^{90} - 180 q^{92} - 120 q^{94} + 192 q^{95} - 36 q^{96} - 60 q^{97} - 105 q^{98} + O(q^{100}) \)

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.