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Properties

Label 1872.2.es
Level $1872$
Weight $2$
Character orbit 1872.es
Rep. character $\chi_{1872}(491,\cdot)$
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.es (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

\( 1328 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} + O(q^{10}) \) \( 1328 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} - 4 q^{10} - 6 q^{11} - 20 q^{12} - 2 q^{13} - 12 q^{14} + 2 q^{16} - 12 q^{18} - 12 q^{19} - 12 q^{20} + 18 q^{21} + 2 q^{22} - 54 q^{24} - 48 q^{26} - 20 q^{27} - 12 q^{28} - 6 q^{29} - 10 q^{30} - 6 q^{32} - 12 q^{33} + 12 q^{34} + 30 q^{35} - 6 q^{36} - 12 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} + 6 q^{42} - 4 q^{43} - 6 q^{45} - 12 q^{46} - 16 q^{48} - 1240 q^{49} - 12 q^{50} - 20 q^{51} - 2 q^{52} - 6 q^{54} - 8 q^{55} - 6 q^{58} - 6 q^{59} - 24 q^{60} - 4 q^{61} - 30 q^{62} + 20 q^{64} - 12 q^{65} - 56 q^{66} + 22 q^{69} + 42 q^{70} + 42 q^{72} - 4 q^{75} - 12 q^{77} - 6 q^{78} - 4 q^{81} + 22 q^{82} + 36 q^{84} - 36 q^{85} - 4 q^{87} - 22 q^{88} + 44 q^{90} + 6 q^{91} - 12 q^{92} + 12 q^{93} - 20 q^{94} + 48 q^{96} + 42 q^{98} - 54 q^{99} + O(q^{100}) \)

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.