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Properties

Label 1872.4.ep
Level $1872$
Weight $4$
Character orbit 1872.ep
Rep. character $\chi_{1872}(115,\cdot)$
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.ep (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

\( 4016 q - 2 q^{2} - 2 q^{3} - 4 q^{5} + 24 q^{6} - 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 4016 q - 2 q^{2} - 2 q^{3} - 4 q^{5} + 24 q^{6} - 4 q^{7} - 2 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} - 4 q^{14} + 108 q^{15} - 4 q^{16} - 24 q^{17} + 166 q^{18} - 4 q^{19} + 254 q^{20} - 162 q^{21} - 4 q^{22} - 12 q^{23} - 264 q^{24} - 49400 q^{25} - 264 q^{26} + 388 q^{27} + 120 q^{28} - 4 q^{29} - 256 q^{30} - 2 q^{32} - 8 q^{33} - 34 q^{34} + 746 q^{35} - 2028 q^{36} - 12 q^{37} - 564 q^{38} - 8 q^{39} - 4 q^{40} + 290 q^{42} - 6 q^{43} - 1320 q^{44} + 744 q^{45} + 8 q^{46} - 22 q^{48} - 12 q^{49} + 846 q^{50} - 2 q^{52} - 16 q^{53} + 1854 q^{54} - 8 q^{55} - 6 q^{56} + 108 q^{57} + 1250 q^{58} + 4076 q^{59} + 222 q^{60} + 2 q^{61} - 2946 q^{62} - 4 q^{65} - 204 q^{66} + 2 q^{67} + 258 q^{68} - 6 q^{69} + 1168 q^{70} - 16 q^{71} - 1484 q^{72} - 1818 q^{74} + 656 q^{75} - 130 q^{76} - 1372 q^{77} + 1620 q^{78} + 5510 q^{80} - 4 q^{81} - 12 q^{82} - 4 q^{83} - 1978 q^{84} + 3094 q^{86} - 4 q^{87} - 2048 q^{88} + 516 q^{90} - 694 q^{91} + 2100 q^{92} - 6 q^{93} + 2 q^{94} - 1000 q^{95} - 5644 q^{96} - 4 q^{97} + 3964 q^{98} - 4374 q^{99} + O(q^{100}) \)

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.