↑

Properties

Label 1800.2.ce
Level $1800$
Weight $2$
Character orbit 1800.ce
Rep. character $\chi_{1800}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $848$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

Total New Old
Modular forms 1488 880 608
Cusp forms 1392 848 544
Eisenstein series 96 32 64

Trace form

\( 848 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 8 q^{8} + O(q^{10}) \) \( 848 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 8 q^{8} - 8 q^{11} + 10 q^{12} - 4 q^{16} + 16 q^{17} - 20 q^{18} - 6 q^{22} + 48 q^{26} + 8 q^{27} - 8 q^{28} + 22 q^{32} - 4 q^{33} - 56 q^{36} + 26 q^{38} - 8 q^{41} + 66 q^{42} + 4 q^{43} + 32 q^{46} + 38 q^{48} - 16 q^{51} - 14 q^{52} - 60 q^{56} - 16 q^{57} - 6 q^{58} + 76 q^{62} + 136 q^{66} + 4 q^{67} + 46 q^{68} - 38 q^{72} + 16 q^{73} + 36 q^{76} + 38 q^{78} + 16 q^{81} + 4 q^{83} + 68 q^{86} + 42 q^{88} - 32 q^{91} - 52 q^{92} - 240 q^{96} + 4 q^{97} + 140 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)