Properties

Label 1872.4.el
Level $1872$
Weight $4$
Character orbit 1872.el
Rep. character $\chi_{1872}(461,\cdot)$
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.el (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

\( 4016 q - 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{6} + 18 q^{8} + O(q^{10}) \) \( 4016 q - 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{6} + 18 q^{8} + 4 q^{10} - 6 q^{11} - 2 q^{13} - 12 q^{14} - 8 q^{15} + 2 q^{16} - 222 q^{18} - 4 q^{19} - 6 q^{20} + 46 q^{21} + 2 q^{22} - 480 q^{24} - 49400 q^{25} + 768 q^{26} + 388 q^{27} - 136 q^{28} - 6 q^{29} + 494 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} - 18 q^{34} - 750 q^{35} + 278 q^{36} - 4 q^{37} + 1788 q^{38} - 4 q^{40} - 682 q^{42} - 384 q^{44} + 498 q^{45} + 8 q^{46} - 12 q^{47} - 42 q^{48} + 744 q^{50} - 2 q^{52} - 2886 q^{54} + 1500 q^{55} - 12 q^{56} + 108 q^{57} + 560 q^{58} - 6126 q^{59} + 296 q^{60} - 4 q^{61} - 2934 q^{62} + 2736 q^{63} - 12 q^{65} - 2404 q^{66} - 4 q^{67} - 6 q^{69} + 1838 q^{70} + 4230 q^{72} - 256 q^{75} + 254 q^{76} - 3834 q^{78} - 8 q^{79} - 1134 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} + 1098 q^{84} + 252 q^{85} - 6 q^{86} - 1030 q^{88} + 516 q^{90} + 678 q^{91} - 12 q^{92} - 4328 q^{93} - 4 q^{94} - 12 q^{95} - 610 q^{96} - 4 q^{97} + 48 q^{98} - 4374 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.