Properties

Label 1872.2.hh
Level $1872$
Weight $2$
Character orbit 1872.hh
Rep. character $\chi_{1872}(5,\cdot)$
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.hh (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

\( 1328 q - 6 q^{2} - 8 q^{3} - 12 q^{5} - 6 q^{6} + O(q^{10}) \) \( 1328 q - 6 q^{2} - 8 q^{3} - 12 q^{5} - 6 q^{6} - 16 q^{10} - 2 q^{13} - 12 q^{14} - 8 q^{15} - 4 q^{16} + 6 q^{18} - 6 q^{20} - 4 q^{22} + 24 q^{24} + 632 q^{25} - 8 q^{27} + 8 q^{28} - 12 q^{29} - 20 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{36} + 84 q^{38} - 4 q^{40} - 28 q^{42} - 16 q^{46} - 12 q^{47} + 12 q^{48} + 42 q^{50} - 2 q^{52} - 50 q^{54} + 24 q^{57} - 12 q^{58} - 80 q^{60} - 4 q^{61} - 36 q^{63} - 12 q^{65} - 28 q^{66} - 60 q^{68} - 40 q^{70} + 46 q^{72} - 180 q^{74} - 20 q^{75} + 6 q^{76} - 52 q^{78} - 8 q^{79} - 16 q^{81} + 82 q^{84} + 102 q^{86} - 32 q^{88} - 12 q^{90} + 20 q^{91} - 12 q^{92} - 4 q^{94} - 8 q^{96} - 4 q^{97} - 36 q^{99} + O(q^{100}) \)

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

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