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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

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

Display 100 coefficients 10 coefficients

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

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