↑

Properties

Label 1872.2.hd
Level $1872$
Weight $2$
Character orbit 1872.hd
Rep. character $\chi_{1872}(643,\cdot)$
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.hd (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

\( 1328 q - 2 q^{2} - 2 q^{3} - 8 q^{6} - 4 q^{7} - 14 q^{8} + O(q^{10}) \) \( 1328 q - 2 q^{2} - 2 q^{3} - 8 q^{6} - 4 q^{7} - 14 q^{8} - 16 q^{10} - 2 q^{13} - 4 q^{14} - 12 q^{15} - 4 q^{16} - 24 q^{17} - 14 q^{18} - 12 q^{19} - 18 q^{20} - 14 q^{21} - 4 q^{22} - 12 q^{23} + 632 q^{25} + 4 q^{26} + 28 q^{27} - 4 q^{29} + 4 q^{30} - 2 q^{32} - 8 q^{33} - 10 q^{34} - 34 q^{35} - 60 q^{36} - 4 q^{37} - 24 q^{38} - 8 q^{39} - 4 q^{40} - 10 q^{42} - 6 q^{43} + 32 q^{44} + 8 q^{45} - 4 q^{46} - 22 q^{48} - 12 q^{49} - 10 q^{50} - 2 q^{52} - 16 q^{53} - 2 q^{54} - 8 q^{55} - 6 q^{56} - 12 q^{57} - 54 q^{58} + 2 q^{60} + 2 q^{61} - 30 q^{62} - 4 q^{65} + 48 q^{66} - 6 q^{67} + 18 q^{68} - 6 q^{69} - 4 q^{70} - 16 q^{71} - 100 q^{72} + 30 q^{74} - 8 q^{75} + 6 q^{76} + 28 q^{77} - 24 q^{78} + 26 q^{80} - 4 q^{81} - 12 q^{82} + 2 q^{84} + 16 q^{85} - 34 q^{86} - 4 q^{87} + 32 q^{88} - 24 q^{90} + 6 q^{91} + 180 q^{92} - 110 q^{93} + 2 q^{94} + 40 q^{95} + 84 q^{96} - 4 q^{97} + 176 q^{98} - 54 q^{99} + O(q^{100}) \)

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.