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Properties

Label 1872.4.gr
Level $1872$
Weight $4$
Character orbit 1872.gr
Rep. character $\chi_{1872}(133,\cdot)$
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.gr (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

\( 4016 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 4 q^{5} - 32 q^{6} - 16 q^{8} + O(q^{10}) \) \( 4016 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 4 q^{5} - 32 q^{6} - 16 q^{8} - 4 q^{10} - 4 q^{11} - 164 q^{12} - 2 q^{13} + 28 q^{14} - 4 q^{15} - 4 q^{16} - 8 q^{17} + 8 q^{18} - 4 q^{19} + 2 q^{20} + 46 q^{21} - 4 q^{22} + 734 q^{24} - 280 q^{26} + 124 q^{27} + 252 q^{28} - 4 q^{29} - 66 q^{30} - 8 q^{31} - 4 q^{32} - 4 q^{33} + 12 q^{34} - 254 q^{35} - 4 q^{37} - 4 q^{38} - 4 q^{40} - 1206 q^{42} + 2 q^{43} - 16 q^{44} + 248 q^{45} + 28 q^{46} - 8 q^{47} - 2466 q^{48} + 96044 q^{49} + 2166 q^{50} + 100 q^{51} - 2 q^{52} - 16 q^{53} - 2 q^{54} + 316 q^{56} - 2380 q^{58} - 4084 q^{59} - 136 q^{60} + 2 q^{61} + 990 q^{62} - 2748 q^{63} - 556 q^{64} - 4 q^{65} - 7716 q^{66} + 2 q^{67} + 1280 q^{68} - 110 q^{69} - 690 q^{70} + 4998 q^{72} + 1822 q^{74} + 552 q^{75} + 2 q^{76} + 1368 q^{77} - 4676 q^{78} - 8 q^{79} - 4644 q^{80} - 4 q^{81} - 674 q^{82} - 4 q^{83} - 5858 q^{84} - 504 q^{85} - 524 q^{86} - 4180 q^{88} - 4692 q^{90} + 678 q^{91} + 252 q^{92} - 8438 q^{93} - 30 q^{94} + 24312 q^{95} - 9864 q^{96} + 4 q^{97} - 722 q^{98} - 3862 q^{99} + O(q^{100}) \)

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.