↑

Properties

Label 1200.4.bf
Level $1200$
Weight $4$
Character orbit 1200.bf
Rep. character $\chi_{1200}(293,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $856$
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.bf (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1464 872 592
Cusp forms 1416 856 560
Eisenstein series 48 16 32

Trace form

\( 856 q + 4 q^{3} + 24 q^{4} - 4 q^{6} + O(q^{10}) \) \( 856 q + 4 q^{3} + 24 q^{4} - 4 q^{6} + 56 q^{12} + 8 q^{13} + 256 q^{16} - 252 q^{18} + 48 q^{19} - 4 q^{21} + 188 q^{22} + 108 q^{24} + 4 q^{27} + 692 q^{28} - 16 q^{31} + 4 q^{33} - 1848 q^{34} - 260 q^{36} + 8 q^{37} - 216 q^{39} - 640 q^{42} + 160 q^{46} + 256 q^{48} - 4 q^{51} + 1136 q^{52} - 2112 q^{54} + 108 q^{57} - 2340 q^{58} - 1832 q^{61} + 1376 q^{63} - 3192 q^{64} - 3300 q^{66} + 108 q^{69} + 1608 q^{72} + 5200 q^{76} + 2172 q^{78} - 8 q^{81} - 1776 q^{82} - 6084 q^{84} - 108 q^{87} + 6132 q^{88} - 8 q^{91} + 112 q^{93} + 840 q^{94} - 2796 q^{96} + 8 q^{97} + 5312 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)