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Properties

Label 504.4.p
Level $504$
Weight $4$
Character orbit 504.p
Rep. character $\chi_{504}(307,\cdot)$
Character field $\Q$
Dimension $118$
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.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 296 122 174
Cusp forms 280 118 162
Eisenstein series 16 4 12

Trace form

\( 118 q + 3 q^{2} - 7 q^{4} - 57 q^{8} + O(q^{10}) \) \( 118 q + 3 q^{2} - 7 q^{4} - 57 q^{8} + 24 q^{11} - 51 q^{14} + 69 q^{16} - 208 q^{22} + 2746 q^{25} + 551 q^{28} - 417 q^{32} + 480 q^{35} + 400 q^{43} + 108 q^{44} - 422 q^{46} + 358 q^{49} + 585 q^{50} + 453 q^{56} - 936 q^{58} - 1303 q^{64} + 504 q^{65} + 2048 q^{67} - 1296 q^{70} - 492 q^{74} + 4620 q^{86} - 256 q^{88} + 1960 q^{91} - 3654 q^{92} + 2811 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)