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Properties

Label 1872.2.ei
Level $1872$
Weight $2$
Character orbit 1872.ei
Rep. character $\chi_{1872}(331,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1328$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.ei (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1872 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1328 1328 0
Eisenstein series 32 32 0

Trace form

\( 1328 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 4 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 1328 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 4 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{8} - 8 q^{10} + 2 q^{11} - 2 q^{13} - 4 q^{14} + 12 q^{15} + 2 q^{16} - 24 q^{17} + 10 q^{18} - 4 q^{19} + 14 q^{20} + 18 q^{21} + 2 q^{22} + 24 q^{24} - 632 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{29} + 14 q^{30} - 2 q^{32} - 8 q^{33} + 2 q^{34} + 26 q^{35} - 18 q^{36} - 12 q^{37} + 24 q^{38} - 8 q^{39} - 4 q^{40} + 38 q^{42} - 48 q^{44} - 6 q^{45} - 4 q^{46} + 38 q^{48} + 48 q^{50} - 2 q^{52} - 16 q^{53} - 66 q^{54} - 8 q^{55} + 12 q^{57} + 8 q^{58} - 22 q^{59} - 4 q^{61} - 30 q^{62} - 4 q^{65} + 48 q^{66} - 4 q^{67} - 36 q^{68} - 6 q^{69} - 2 q^{70} - 16 q^{71} - 74 q^{72} - 60 q^{74} - 16 q^{75} + 14 q^{76} - 28 q^{77} - 102 q^{78} - 10 q^{80} - 4 q^{81} - 12 q^{82} - 4 q^{83} - 46 q^{84} - 36 q^{85} + 10 q^{86} - 4 q^{87} + 10 q^{88} + 24 q^{90} - 22 q^{91} + 180 q^{92} + 12 q^{93} - 4 q^{94} + 20 q^{95} + 86 q^{96} - 4 q^{97} - 128 q^{98} + 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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