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Properties

Label 3800.2.bm
Level $3800$
Weight $2$
Character orbit 3800.bm
Rep. character $\chi_{3800}(501,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $748$
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
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 772 452
Cusp forms 1176 748 428
Eisenstein series 48 24 24

Trace form

\( 748 q + q^{2} - q^{4} - q^{6} + 8 q^{7} - 2 q^{8} + 364 q^{9} + O(q^{10}) \) \( 748 q + q^{2} - q^{4} - q^{6} + 8 q^{7} - 2 q^{8} + 364 q^{9} + 10 q^{12} - 8 q^{14} - q^{16} + 2 q^{17} + 20 q^{18} + 9 q^{22} + 2 q^{23} - 9 q^{24} - 12 q^{26} + 12 q^{28} + 16 q^{31} + 21 q^{32} + 4 q^{33} - 4 q^{34} + 44 q^{36} - 20 q^{38} - 28 q^{39} - 2 q^{41} + 18 q^{42} - 15 q^{44} - 32 q^{46} - 10 q^{47} + 39 q^{48} + 668 q^{49} + 6 q^{52} + 9 q^{54} + 40 q^{56} + 14 q^{57} - 28 q^{58} + 38 q^{62} + 28 q^{63} - 22 q^{64} - 17 q^{66} + 8 q^{68} + 22 q^{71} - 36 q^{72} - 6 q^{73} - 18 q^{74} - 69 q^{76} + 16 q^{78} - 34 q^{79} - 342 q^{81} + 11 q^{82} - 108 q^{84} - 36 q^{86} - 36 q^{87} + 58 q^{88} + 2 q^{89} - 22 q^{92} + 100 q^{94} - 130 q^{96} - 14 q^{97} + 47 q^{98} + O(q^{100}) \)

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.

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

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)