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Properties

Label 1872.2.ha
Level $1872$
Weight $2$
Character orbit 1872.ha
Rep. character $\chi_{1872}(419,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1328$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.ha (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

\( 1328 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 12 q^{5} + 10 q^{6} - 8 q^{7} + O(q^{10}) \) \( 1328 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 12 q^{5} + 10 q^{6} - 8 q^{7} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 2 q^{13} - 12 q^{14} + 2 q^{16} - 12 q^{18} - 4 q^{19} - 14 q^{21} + 2 q^{22} + 14 q^{24} - 48 q^{26} + 4 q^{27} - 20 q^{28} - 6 q^{29} + 6 q^{30} - 6 q^{32} - 4 q^{33} - 8 q^{34} - 30 q^{35} - 6 q^{36} - 4 q^{37} - 12 q^{38} - 32 q^{39} - 4 q^{40} - 90 q^{42} - 4 q^{43} + 18 q^{45} + 4 q^{46} - 68 q^{48} + 1224 q^{49} - 20 q^{51} - 2 q^{52} - 2 q^{54} - 8 q^{55} + 38 q^{58} + 66 q^{59} - 4 q^{61} - 6 q^{62} + 20 q^{64} - 12 q^{65} + 80 q^{66} - 4 q^{67} + 22 q^{69} + 10 q^{70} - 74 q^{72} - 24 q^{75} - 4 q^{76} - 12 q^{77} - 66 q^{78} - 96 q^{80} - 4 q^{81} - 30 q^{82} - 12 q^{83} - 92 q^{84} - 8 q^{85} - 12 q^{86} - 4 q^{87} + 26 q^{88} - 28 q^{90} - 22 q^{91} - 12 q^{92} - 44 q^{93} + 12 q^{94} - 136 q^{96} - 8 q^{97} - 66 q^{98} + 38 q^{99} + O(q^{100}) \)

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.