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Properties

Label 504.4.ch
Level $504$
Weight $4$
Character orbit 504.ch
Rep. character $\chi_{504}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.ch (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
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 592 192 400
Cusp forms 560 192 368
Eisenstein series 32 0 32

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 60 q^{16} + 528 q^{22} + 2400 q^{25} - 900 q^{28} - 2340 q^{40} + 720 q^{46} - 720 q^{49} + 2484 q^{52} - 84 q^{58} - 1368 q^{64} + 588 q^{70} + 1296 q^{73} - 240 q^{79} + 612 q^{82} + 3108 q^{88} - 8964 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)