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Properties

Label 504.4.bs
Level $504$
Weight $4$
Character orbit 504.bs
Rep. character $\chi_{504}(257,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 592 144 448
Cusp forms 560 144 416
Eisenstein series 32 0 32

Trace form

\( 144 q - 28 q^{9} + O(q^{10}) \) \( 144 q - 28 q^{9} - 88 q^{15} - 208 q^{21} - 156 q^{23} - 1800 q^{25} + 414 q^{27} + 126 q^{29} + 974 q^{39} + 618 q^{41} - 126 q^{43} - 1686 q^{45} - 396 q^{47} - 198 q^{49} + 276 q^{51} + 1092 q^{53} - 692 q^{57} - 2858 q^{63} + 594 q^{75} + 1476 q^{77} - 252 q^{79} - 768 q^{81} - 312 q^{87} - 954 q^{89} + 990 q^{91} - 608 q^{93} + 896 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)