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Properties

Label 3800.2.da
Level $3800$
Weight $2$
Character orbit 3800.da
Rep. character $\chi_{3800}(149,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2136$
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.da (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 3672 2184 1488
Cusp forms 3528 2136 1392
Eisenstein series 144 48 96

Trace form

\( 2136 q + 24 q^{9} + O(q^{10}) \) \( 2136 q + 24 q^{9} + 18 q^{14} - 24 q^{16} + 72 q^{24} - 54 q^{26} + 60 q^{31} - 36 q^{34} - 78 q^{36} + 48 q^{39} - 24 q^{41} + 36 q^{44} - 6 q^{46} + 1008 q^{49} + 36 q^{54} + 60 q^{56} + 54 q^{64} - 48 q^{66} - 24 q^{71} + 126 q^{74} + 60 q^{76} + 24 q^{79} - 60 q^{81} - 6 q^{84} + 36 q^{86} + 24 q^{89} - 12 q^{94} + 72 q^{96} + O(q^{100}) \)

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

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