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Properties

Label 3800.2.bg
Level $3800$
Weight $2$
Character orbit 3800.bg
Rep. character $\chi_{3800}(1699,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $712$
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.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 1224 728 496
Cusp forms 1176 712 464
Eisenstein series 48 16 32

Trace form

\( 712 q + 6 q^{4} - 6 q^{6} - 344 q^{9} + O(q^{10}) \) \( 712 q + 6 q^{4} - 6 q^{6} - 344 q^{9} - 16 q^{11} - 24 q^{14} + 2 q^{16} + 24 q^{19} - 42 q^{24} + 52 q^{26} - 42 q^{34} + 52 q^{36} - 12 q^{41} + 54 q^{44} + 680 q^{49} + 36 q^{51} + 12 q^{59} + 60 q^{64} - 66 q^{66} + 36 q^{74} + 76 q^{76} - 316 q^{81} - 174 q^{86} + 12 q^{89} + 72 q^{91} + 52 q^{96} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)