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Properties

Label 1872.4.eg
Level $1872$
Weight $4$
Character orbit 1872.eg
Rep. character $\chi_{1872}(187,\cdot)$
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.eg (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

\( 4016 q - 2 q^{2} - 8 q^{3} - 4 q^{5} - 18 q^{6} - 4 q^{7} - 20 q^{8} + O(q^{10}) \) \( 4016 q - 2 q^{2} - 8 q^{3} - 4 q^{5} - 18 q^{6} - 4 q^{7} - 20 q^{8} + 64 q^{10} - 4 q^{11} - 2 q^{13} - 4 q^{14} + 108 q^{15} - 4 q^{16} + 166 q^{18} - 16 q^{19} + 254 q^{20} - 4 q^{22} - 264 q^{24} - 49400 q^{25} + 504 q^{26} - 8 q^{27} - 264 q^{28} - 4 q^{29} + 500 q^{30} - 2 q^{32} - 8 q^{33} + 14 q^{34} - 16 q^{35} + 984 q^{36} - 612 q^{38} - 8 q^{39} - 4 q^{40} + 332 q^{42} + 2616 q^{44} - 40 q^{46} - 28 q^{48} + 846 q^{50} - 2 q^{52} - 16 q^{53} + 1806 q^{54} - 32 q^{55} - 216 q^{57} - 628 q^{58} - 2044 q^{59} - 252 q^{60} - 4 q^{61} - 4 q^{65} + 1092 q^{66} - 4 q^{67} + 252 q^{68} + 1168 q^{70} - 16 q^{71} - 710 q^{72} + 3636 q^{74} + 500 q^{75} - 130 q^{76} + 2744 q^{77} + 7476 q^{78} - 9544 q^{80} - 16 q^{81} - 4 q^{83} + 7526 q^{84} + 2998 q^{86} - 16 q^{87} - 2048 q^{88} + 468 q^{90} + 1364 q^{91} - 516 q^{92} - 4 q^{94} - 1000 q^{95} - 3532 q^{96} - 4 q^{97} + 3916 q^{98} + O(q^{100}) \)

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.