Properties

Label 252.4.bf
Level $252$
Weight $4$
Character orbit 252.bf
Rep. character $\chi_{252}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
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 304 124 180
Cusp forms 272 116 156
Eisenstein series 32 8 24

Trace form

\( 116q + 2q^{2} + 4q^{4} + 6q^{5} + 80q^{8} + O(q^{10}) \) \( 116q + 2q^{2} + 4q^{4} + 6q^{5} + 80q^{8} - 12q^{10} - 86q^{14} - 44q^{16} + 6q^{17} + 344q^{22} + 1332q^{25} + 354q^{26} - 452q^{28} - 448q^{29} - 68q^{32} - 246q^{37} + 126q^{38} + 792q^{40} - 220q^{44} + 352q^{46} + 844q^{49} - 1628q^{50} + 108q^{52} + 574q^{53} + 1352q^{56} - 576q^{58} + 294q^{61} - 1112q^{64} - 156q^{65} - 1368q^{68} + 740q^{70} - 978q^{73} - 822q^{74} + 2314q^{77} - 1056q^{80} - 3360q^{82} - 388q^{85} + 130q^{86} - 1312q^{88} + 3186q^{89} - 2360q^{92} + 2184q^{94} - 2996q^{98} + O(q^{100}) \)

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)