Properties

Label 252.4.bi
Level $252$
Weight $4$
Character orbit 252.bi
Rep. character $\chi_{252}(139,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

Trace form

\( 280q - 2q^{2} - 2q^{4} - 8q^{8} - 8q^{9} + O(q^{10}) \) \( 280q - 2q^{2} - 2q^{4} - 8q^{8} - 8q^{9} - 42q^{14} - 2q^{16} - 58q^{18} + 118q^{21} - 34q^{22} + 3096q^{25} - 132q^{28} - 60q^{29} - 88q^{30} - 752q^{32} - 1166q^{36} - 16q^{37} - 260q^{42} + 1276q^{44} - 40q^{46} - 2q^{49} - 340q^{50} - 16q^{53} + 1500q^{56} - 648q^{57} + 30q^{58} - 88q^{60} - 8q^{64} - 772q^{65} - 586q^{70} + 44q^{72} - 536q^{74} - 1702q^{77} - 6048q^{78} + 3376q^{81} - 3058q^{84} + 496q^{85} + 1348q^{86} + 1022q^{88} - 3226q^{92} - 12q^{93} + 4540q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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