↑

Properties

Label 1872.4.hf
Level $1872$
Weight $4$
Character orbit 1872.hf
Rep. character $\chi_{1872}(605,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4016$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.hf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1872 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).

Total New Old
Modular forms 4048 4048 0
Cusp forms 4016 4016 0
Eisenstein series 32 32 0

Trace form

\( 4016 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 12 q^{5} + 42 q^{6} - 18 q^{8} + O(q^{10}) \) \( 4016 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 12 q^{5} + 42 q^{6} - 18 q^{8} - 28 q^{10} - 6 q^{11} - 2 q^{13} - 12 q^{14} - 8 q^{15} + 2 q^{16} + 150 q^{18} - 12 q^{19} - 6 q^{20} - 162 q^{21} + 2 q^{22} - 264 q^{24} + 49400 q^{25} + 864 q^{26} - 404 q^{27} - 136 q^{28} - 6 q^{29} - 506 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} - 18 q^{34} + 750 q^{35} - 290 q^{36} - 12 q^{37} - 1788 q^{38} - 4 q^{40} - 682 q^{42} + 384 q^{44} - 6 q^{45} + 8 q^{46} - 12 q^{47} - 42 q^{48} - 756 q^{50} - 2 q^{52} + 2878 q^{54} - 1500 q^{55} - 12 q^{56} - 108 q^{57} + 624 q^{58} - 6 q^{59} - 560 q^{60} - 4 q^{61} - 2934 q^{62} + 2736 q^{63} - 12 q^{65} + 188 q^{66} - 6 q^{69} + 902 q^{70} + 1786 q^{72} + 244 q^{75} - 258 q^{76} + 506 q^{78} - 8 q^{79} + 15054 q^{80} - 4 q^{81} - 12 q^{82} + 4750 q^{84} + 744 q^{85} - 6 q^{86} + 1018 q^{88} - 516 q^{90} - 694 q^{91} - 12 q^{92} - 168 q^{93} - 4 q^{94} - 12 q^{95} - 4982 q^{96} - 4 q^{97} + 48 q^{98} + 3846 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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