↑

Properties

Label 3800.2.ed
Level $3800$
Weight $2$
Character orbit 3800.ed
Rep. character $\chi_{3800}(43,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $4272$
Sturm bound $1200$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.ed (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 7344 4368 2976
Cusp forms 7056 4272 2784
Eisenstein series 288 96 192

Trace form

\( 4272 q + 12 q^{2} + 24 q^{3} - 48 q^{6} + 6 q^{8} + O(q^{10}) \) \( 4272 q + 12 q^{2} + 24 q^{3} - 48 q^{6} + 6 q^{8} - 24 q^{11} + 6 q^{12} + 24 q^{17} + 24 q^{18} + 84 q^{26} + 12 q^{27} - 48 q^{28} - 18 q^{32} - 12 q^{33} - 120 q^{36} + 78 q^{38} - 48 q^{41} + 48 q^{42} + 24 q^{43} - 12 q^{46} - 72 q^{48} + 48 q^{51} + 12 q^{52} - 48 q^{56} + 24 q^{57} + 168 q^{58} + 84 q^{62} + 48 q^{66} + 24 q^{67} + 6 q^{68} + 240 q^{72} + 24 q^{73} - 168 q^{76} + 90 q^{78} - 48 q^{81} + 132 q^{82} + 12 q^{83} - 240 q^{86} - 90 q^{88} - 48 q^{91} + 132 q^{92} + 144 q^{96} + 24 q^{97} - 18 q^{98} + O(q^{100}) \)

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.

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

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