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Properties

Label 1872.4.en
Level $1872$
Weight $4$
Character orbit 1872.en
Rep. character $\chi_{1872}(317,\cdot)$
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.en (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

\( 4016 q - 6 q^{2} - 8 q^{3} + 10 q^{6} + O(q^{10}) \) \( 4016 q - 6 q^{2} - 8 q^{3} + 10 q^{6} + 64 q^{10} - 12 q^{11} - 2 q^{13} - 12 q^{14} - 8 q^{15} - 4 q^{16} - 174 q^{18} - 16 q^{19} - 6 q^{20} - 116 q^{21} - 4 q^{22} - 480 q^{24} - 49400 q^{25} - 8 q^{27} + 248 q^{28} - 12 q^{29} + 500 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} - 18 q^{34} - 1816 q^{36} - 16 q^{37} + 1644 q^{38} - 4 q^{40} + 332 q^{42} + 492 q^{45} - 40 q^{46} - 12 q^{47} + 12 q^{48} - 2454 q^{50} - 2 q^{52} + 330 q^{54} - 216 q^{57} + 560 q^{58} + 6108 q^{59} - 400 q^{60} - 4 q^{61} - 1380 q^{63} - 12 q^{65} - 1108 q^{66} - 4 q^{67} - 780 q^{68} - 172 q^{70} - 4806 q^{72} + 10908 q^{74} + 500 q^{75} - 130 q^{76} - 480 q^{78} - 8 q^{79} - 16 q^{81} - 12 q^{83} - 5790 q^{84} - 504 q^{85} + 8310 q^{86} + 2048 q^{88} + 468 q^{90} - 1380 q^{91} - 12 q^{92} - 4172 q^{93} - 4 q^{94} + 6704 q^{96} - 4 q^{97} + O(q^{100}) \)

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.