↑

Properties

Label 1872.2.gy
Level $1872$
Weight $2$
Character orbit 1872.gy
Rep. character $\chi_{1872}(277,\cdot)$
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.gy (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

\( 1328 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} + O(q^{10}) \) \( 1328 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 2 q^{13} - 12 q^{14} - 12 q^{15} + 2 q^{16} - 8 q^{17} + 12 q^{18} - 12 q^{19} - 18 q^{21} + 2 q^{22} - 54 q^{24} + 8 q^{26} + 4 q^{27} - 12 q^{28} + 2 q^{29} - 10 q^{30} - 6 q^{32} - 12 q^{33} - 12 q^{34} + 6 q^{35} - 6 q^{36} - 12 q^{37} - 4 q^{38} - 4 q^{40} - 90 q^{42} - 4 q^{43} - 6 q^{45} - 12 q^{46} + 64 q^{48} + 1224 q^{49} + 4 q^{51} - 2 q^{52} - 16 q^{53} - 6 q^{54} + 48 q^{56} - 6 q^{58} - 6 q^{59} + 24 q^{60} - 4 q^{61} - 2 q^{62} - 12 q^{63} + 20 q^{64} - 4 q^{65} + 40 q^{66} - 24 q^{68} + 22 q^{69} - 42 q^{70} - 54 q^{72} + 52 q^{74} - 4 q^{75} - 32 q^{77} + 70 q^{78} - 8 q^{79} - 12 q^{80} - 4 q^{81} + 6 q^{82} - 48 q^{84} + 24 q^{85} + 26 q^{88} - 60 q^{90} - 22 q^{91} + 12 q^{92} - 24 q^{93} - 20 q^{94} + 132 q^{95} - 48 q^{96} - 54 q^{98} + 54 q^{99} + O(q^{100}) \)

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.