↑

Properties

Label 1200.4.db
Level $1200$
Weight $4$
Character orbit 1200.db
Rep. character $\chi_{1200}(11,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $5728$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.db (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

Total New Old
Modular forms 5792 5792 0
Cusp forms 5728 5728 0
Eisenstein series 64 64 0

Trace form

\( 5728 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 64 q^{7} + O(q^{10}) \) \( 5728 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 64 q^{7} - 16 q^{10} - 6 q^{12} - 12 q^{13} - 12 q^{16} + 16 q^{18} - 12 q^{19} - 168 q^{21} - 444 q^{22} - 16 q^{24} - 6 q^{27} - 780 q^{28} + 322 q^{30} - 12 q^{33} - 364 q^{34} - 922 q^{36} - 12 q^{37} - 12 q^{39} - 652 q^{40} - 1302 q^{42} + 832 q^{43} + 242 q^{45} - 76 q^{46} + 3660 q^{48} + 271200 q^{49} - 124 q^{51} + 1860 q^{52} - 6 q^{54} - 320 q^{55} + 2004 q^{58} - 1360 q^{60} - 12 q^{61} - 12 q^{64} - 3728 q^{66} - 12 q^{67} - 114 q^{69} - 1688 q^{70} + 3422 q^{72} - 1714 q^{75} + 4864 q^{76} + 5814 q^{78} - 12 q^{81} + 3512 q^{82} + 2420 q^{84} - 516 q^{85} - 2588 q^{87} - 9756 q^{88} - 342 q^{90} - 4128 q^{91} - 124 q^{93} - 1808 q^{94} - 6 q^{96} - 24 q^{97} + 2900 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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