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Properties

Label 1872.4.ha
Level $1872$
Weight $4$
Character orbit 1872.ha
Rep. character $\chi_{1872}(419,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4016$
Sturm bound $1344$

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Defining parameters

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

\( 4016 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 12 q^{5} - 62 q^{6} - 8 q^{7} + O(q^{10}) \) \( 4016 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 12 q^{5} - 62 q^{6} - 8 q^{7} - 4 q^{10} - 6 q^{11} + 148 q^{12} - 2 q^{13} - 12 q^{14} + 2 q^{16} - 24 q^{18} - 4 q^{19} - 62 q^{21} + 2 q^{22} - 370 q^{24} + 816 q^{26} - 140 q^{27} - 260 q^{28} - 6 q^{29} + 30 q^{30} - 6 q^{32} - 4 q^{33} - 20 q^{34} - 750 q^{35} + 762 q^{36} - 4 q^{37} - 12 q^{38} - 608 q^{39} - 4 q^{40} - 1050 q^{42} - 4 q^{43} + 498 q^{45} + 28 q^{46} + 1180 q^{48} + 192072 q^{49} - 116 q^{51} - 2 q^{52} - 2 q^{54} - 8 q^{55} - 1186 q^{58} + 6114 q^{59} + 120 q^{60} - 4 q^{61} - 2886 q^{62} - 556 q^{64} - 12 q^{65} + 7700 q^{66} - 4 q^{67} + 214 q^{69} + 682 q^{70} + 2950 q^{72} - 360 q^{75} - 4 q^{76} - 12 q^{77} + 4926 q^{78} - 13920 q^{80} - 4 q^{81} - 738 q^{82} - 12 q^{83} + 3796 q^{84} - 248 q^{85} - 12 q^{86} - 4 q^{87} - 2086 q^{88} + 3524 q^{90} - 694 q^{91} - 12 q^{92} + 4324 q^{93} + 60 q^{94} + 9848 q^{96} - 8 q^{97} - 2154 q^{98} - 6778 q^{99} + O(q^{100}) \)

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.