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Properties

Label 3800.2.eq
Level $3800$
Weight $2$
Character orbit 3800.eq
Rep. character $\chi_{3800}(373,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $9536$
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.eq (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3800 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 9664 9664 0
Cusp forms 9536 9536 0
Eisenstein series 128 128 0

Trace form

\( 9536 q - 24 q^{2} - 10 q^{4} - 6 q^{6} - 64 q^{7} - 20 q^{9} + O(q^{10}) \) \( 9536 q - 24 q^{2} - 10 q^{4} - 6 q^{6} - 64 q^{7} - 20 q^{9} - 24 q^{10} - 30 q^{14} - 48 q^{15} - 6 q^{16} - 16 q^{17} - 8 q^{20} - 36 q^{22} - 16 q^{23} - 16 q^{25} - 64 q^{26} - 10 q^{28} - 12 q^{30} - 54 q^{32} - 84 q^{33} - 30 q^{34} + 26 q^{36} - 102 q^{38} - 80 q^{39} - 144 q^{40} - 36 q^{41} + 8 q^{42} + 130 q^{44} + 8 q^{47} + 18 q^{48} - 24 q^{52} - 10 q^{54} - 36 q^{55} - 20 q^{57} - 232 q^{58} - 24 q^{60} - 52 q^{62} - 68 q^{63} - 100 q^{64} - 30 q^{66} + 12 q^{68} - 24 q^{70} - 36 q^{71} + 114 q^{72} - 16 q^{73} - 48 q^{76} - 36 q^{78} - 60 q^{79} + 32 q^{80} - 1140 q^{81} + 10 q^{82} - 18 q^{86} + 72 q^{87} - 60 q^{89} - 384 q^{90} + 98 q^{92} - 76 q^{95} - 64 q^{96} - 48 q^{97} - 18 q^{98} + O(q^{100}) \)

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.