Properties

Label 3800.2.bx
Level $3800$
Weight $2$
Character orbit 3800.bx
Rep. character $\chi_{3800}(531,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2384$
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.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3800 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 2416 2416 0
Cusp forms 2384 2384 0
Eisenstein series 32 32 0

Trace form

\( 2384 q - 6 q^{4} - 14 q^{6} + 576 q^{9} + O(q^{10}) \) \( 2384 q - 6 q^{4} - 14 q^{6} + 576 q^{9} - 12 q^{11} - 6 q^{16} - 12 q^{17} - 6 q^{19} - 14 q^{20} - 56 q^{24} - 16 q^{25} + 12 q^{26} + 30 q^{28} - 34 q^{30} + 40 q^{35} - 2 q^{36} + 9 q^{38} + 26 q^{42} - 32 q^{43} + 52 q^{44} - 2320 q^{49} + 28 q^{54} - 28 q^{57} + 32 q^{58} + 32 q^{62} + 24 q^{64} - 2 q^{66} - 28 q^{68} - 12 q^{73} + 20 q^{74} + 20 q^{76} - 18 q^{80} - 600 q^{81} - 124 q^{82} + 68 q^{83} + 18 q^{92} + 32 q^{96} + 16 q^{99} + O(q^{100}) \)

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

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