Properties

Label 252.4.ba
Level $252$
Weight $4$
Character orbit 252.ba
Rep. character $\chi_{252}(155,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
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 296 216 80
Cusp forms 280 216 64
Eisenstein series 16 0 16

Trace form

\( 216q - 30q^{6} - 20q^{9} + O(q^{10}) \) \( 216q - 30q^{6} - 20q^{9} - 156q^{12} + 290q^{18} + 462q^{20} + 382q^{24} + 2700q^{25} - 716q^{30} - 690q^{32} + 892q^{33} + 396q^{34} - 412q^{36} + 180q^{40} + 300q^{41} + 140q^{42} + 984q^{45} - 72q^{46} + 1652q^{48} + 5292q^{49} + 3198q^{50} + 918q^{52} + 1826q^{54} - 172q^{57} + 594q^{58} + 2036q^{60} - 828q^{64} - 696q^{65} - 7446q^{66} - 4602q^{68} + 744q^{69} - 4870q^{72} + 1656q^{73} - 9072q^{74} + 1116q^{76} - 4268q^{78} - 1996q^{81} - 1404q^{82} - 490q^{84} + 4170q^{86} - 2088q^{88} + 15320q^{90} + 9462q^{92} - 672q^{93} - 306q^{94} + 3280q^{96} - 36q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)