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Properties

Label 3800.2.fh
Level $3800$
Weight $2$
Character orbit 3800.fh
Rep. character $\chi_{3800}(13,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $28608$
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.fh (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3800 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 28992 28992 0
Cusp forms 28608 28608 0
Eisenstein series 384 384 0

Trace form

\( 28608 q - 48 q^{2} - 60 q^{4} - 36 q^{6} - 48 q^{7} - 72 q^{8} - 120 q^{9} + O(q^{10}) \) \( 28608 q - 48 q^{2} - 60 q^{4} - 36 q^{6} - 48 q^{7} - 72 q^{8} - 120 q^{9} - 48 q^{10} - 72 q^{12} - 60 q^{14} - 96 q^{15} - 36 q^{16} - 96 q^{17} - 156 q^{20} - 36 q^{22} - 96 q^{23} - 96 q^{25} - 48 q^{26} + 12 q^{28} - 24 q^{30} - 108 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{36} - 60 q^{38} - 240 q^{39} + 72 q^{40} - 72 q^{41} - 84 q^{42} - 60 q^{44} - 54 q^{46} - 168 q^{47} + 36 q^{48} - 72 q^{50} - 48 q^{52} - 60 q^{54} - 36 q^{55} - 96 q^{57} + 48 q^{58} - 48 q^{60} - 276 q^{62} - 12 q^{63} - 30 q^{64} - 144 q^{65} + 36 q^{66} - 24 q^{68} - 48 q^{70} - 72 q^{71} + 84 q^{72} - 96 q^{73} - 96 q^{76} - 72 q^{78} - 120 q^{79} - 108 q^{80} - 72 q^{81} + 192 q^{82} - 90 q^{84} - 36 q^{86} - 48 q^{87} - 72 q^{88} - 120 q^{89} + 312 q^{90} - 228 q^{92} - 96 q^{95} - 72 q^{96} - 96 q^{97} - 54 q^{98} + O(q^{100}) \)

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.