↑

Properties

Label 1872.2.hm
Level $1872$
Weight $2$
Character orbit 1872.hm
Rep. character $\chi_{1872}(149,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1328$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.hm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1872 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1328 1328 0
Eisenstein series 32 32 0

Trace form

\( 1328 q - 6 q^{2} - 2 q^{3} - 12 q^{5} + 18 q^{8} + O(q^{10}) \) \( 1328 q - 6 q^{2} - 2 q^{3} - 12 q^{5} + 18 q^{8} - 16 q^{10} - 12 q^{11} - 2 q^{13} - 12 q^{14} - 8 q^{15} - 4 q^{16} + 6 q^{18} - 12 q^{19} - 6 q^{20} + 18 q^{21} - 4 q^{22} + 24 q^{24} + 632 q^{25} + 36 q^{26} - 44 q^{27} - 16 q^{28} + 4 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 30 q^{35} - 20 q^{36} - 12 q^{37} + 48 q^{38} - 4 q^{40} - 10 q^{42} - 6 q^{43} - 24 q^{44} - 36 q^{45} - 4 q^{46} - 12 q^{47} + 18 q^{48} - 12 q^{49} - 114 q^{50} - 2 q^{52} - 38 q^{54} - 60 q^{55} - 6 q^{56} - 12 q^{57} + 18 q^{58} - 12 q^{59} + 22 q^{60} + 2 q^{61} + 18 q^{62} - 36 q^{63} - 12 q^{65} - 64 q^{66} - 6 q^{67} + 42 q^{68} - 6 q^{69} - 40 q^{70} - 68 q^{72} - 90 q^{74} - 8 q^{75} + 6 q^{76} + 44 q^{78} - 8 q^{79} + 66 q^{80} - 4 q^{81} - 12 q^{82} - 134 q^{84} - 114 q^{86} - 32 q^{88} - 24 q^{90} - 22 q^{91} - 12 q^{92} - 6 q^{93} + 2 q^{94} - 24 q^{95} - 104 q^{96} - 4 q^{97} - 12 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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