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Properties

Label 3800.2.cy
Level $3800$
Weight $2$
Character orbit 3800.cy
Rep. character $\chi_{3800}(51,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2244$
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.cy (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
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 2316 1356
Cusp forms 3528 2244 1284
Eisenstein series 144 72 72

Trace form

\( 2244 q + 6 q^{2} + 12 q^{3} + 12 q^{4} - 24 q^{6} + 9 q^{8} + 12 q^{9} + O(q^{10}) \) \( 2244 q + 6 q^{2} + 12 q^{3} + 12 q^{4} - 24 q^{6} + 9 q^{8} + 12 q^{9} - 18 q^{11} + 9 q^{12} - 3 q^{14} - 24 q^{16} + 12 q^{17} + 12 q^{19} - 33 q^{26} + 18 q^{27} + 36 q^{28} - 9 q^{32} - 6 q^{33} + 12 q^{34} - 93 q^{36} - 12 q^{38} - 48 q^{41} + 117 q^{42} + 12 q^{43} - 3 q^{44} + 18 q^{46} + 39 q^{48} + 1020 q^{49} - 60 q^{51} - 33 q^{52} + 33 q^{54} + 12 q^{57} + 84 q^{58} + 12 q^{59} + 6 q^{62} - 3 q^{64} + 114 q^{66} + 12 q^{67} + 6 q^{68} - 18 q^{72} - 12 q^{73} - 141 q^{74} - 18 q^{76} - 21 q^{78} - 6 q^{81} - 69 q^{82} + 6 q^{83} - 99 q^{84} + 48 q^{86} + 81 q^{88} + 12 q^{89} + 6 q^{91} - 36 q^{92} - 186 q^{96} + 12 q^{97} - 81 q^{98} - 42 q^{99} + O(q^{100}) \)

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

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