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Properties

Label 504.4.br
Level $504$
Weight $4$
Character orbit 504.br
Rep. character $\chi_{504}(155,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $432$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.br (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(504, [\chi])\).

Total New Old
Modular forms 584 432 152
Cusp forms 568 432 136
Eisenstein series 16 0 16

Trace form

\( 432 q - 30 q^{6} + O(q^{10}) \) \( 432 q - 30 q^{6} - 156 q^{12} - 290 q^{18} + 462 q^{20} + 354 q^{24} - 5400 q^{25} - 264 q^{27} - 396 q^{30} + 690 q^{32} + 464 q^{33} - 396 q^{34} - 828 q^{36} - 180 q^{40} - 120 q^{41} - 140 q^{42} - 72 q^{46} + 792 q^{48} + 10584 q^{49} + 3198 q^{50} - 918 q^{52} - 1826 q^{54} + 344 q^{57} + 594 q^{58} - 6120 q^{59} - 2648 q^{60} + 1908 q^{64} - 4066 q^{66} - 4602 q^{68} - 486 q^{72} + 3612 q^{74} + 6608 q^{75} + 1116 q^{76} - 1280 q^{78} - 920 q^{81} - 1404 q^{82} + 490 q^{84} + 4170 q^{86} - 2088 q^{88} - 9352 q^{90} + 9462 q^{92} + 306 q^{94} + 2896 q^{96} + 5312 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)