↑

Properties

Label 1800.4.cx
Level $1800$
Weight $4$
Character orbit 1800.cx
Rep. character $\chi_{1800}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8608$
Sturm bound $1440$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.cx (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1800 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).

Total New Old
Modular forms 8672 8672 0
Cusp forms 8608 8608 0
Eisenstein series 64 64 0

Trace form

\( 8608 q - 15 q^{2} - 20 q^{3} - 3 q^{4} - 22 q^{6} - 12 q^{9} + O(q^{10}) \) \( 8608 q - 15 q^{2} - 20 q^{3} - 3 q^{4} - 22 q^{6} - 12 q^{9} - 18 q^{11} - 10 q^{12} - 9 q^{14} - 3 q^{16} - 24 q^{19} - 243 q^{20} - 5 q^{22} + 78 q^{24} - 8 q^{25} - 20 q^{27} + 620 q^{28} - 336 q^{30} - 20 q^{33} + 13 q^{34} - 464 q^{36} - 15 q^{38} - 129 q^{40} - 18 q^{41} + 1770 q^{42} + 20 q^{46} - 3065 q^{48} - 206208 q^{49} - 1611 q^{50} + 184 q^{51} - 5 q^{52} + 1109 q^{54} + 3078 q^{56} - 5 q^{58} - 18 q^{59} - 8377 q^{60} - 12 q^{64} - 24 q^{65} - 3226 q^{66} - 10 q^{67} - 1618 q^{70} - 10 q^{72} - 40 q^{73} + 6366 q^{74} + 3342 q^{75} + 120 q^{76} + 5850 q^{78} - 12 q^{81} - 30 q^{83} + 5527 q^{84} - 8349 q^{86} - 5 q^{88} + 579 q^{90} + 4092 q^{91} - 15 q^{92} - 2455 q^{94} - 2623 q^{96} - 10 q^{97} + 2884 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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