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Properties

Label 504.4.r
Level $504$
Weight $4$
Character orbit 504.r
Rep. character $\chi_{504}(169,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $108$
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.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 592 108 484
Cusp forms 560 108 452
Eisenstein series 32 0 32

Trace form

\( 108 q - 2 q^{3} - 30 q^{9} + O(q^{10}) \) \( 108 q - 2 q^{3} - 30 q^{9} - 82 q^{11} - 76 q^{15} + 228 q^{17} + 180 q^{19} + 52 q^{23} - 1350 q^{25} - 596 q^{27} + 348 q^{29} + 954 q^{33} + 840 q^{35} + 308 q^{39} + 30 q^{41} + 342 q^{43} - 36 q^{45} - 1164 q^{47} - 2646 q^{49} - 1450 q^{51} - 1680 q^{53} - 3030 q^{57} - 322 q^{59} - 532 q^{63} + 2336 q^{65} + 774 q^{67} + 1280 q^{69} + 1752 q^{71} - 2484 q^{73} + 3242 q^{75} + 616 q^{77} + 210 q^{81} - 1904 q^{83} + 1656 q^{85} - 3320 q^{87} - 6960 q^{89} - 4196 q^{93} - 3012 q^{95} + 738 q^{97} + 756 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)