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Properties

Label 600.4.d
Level $600$
Weight $4$
Character orbit 600.d
Rep. character $\chi_{600}(349,\cdot)$
Character field $\Q$
Dimension $108$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 600.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(600, [\chi])\).

Total New Old
Modular forms 372 108 264
Cusp forms 348 108 240
Eisenstein series 24 0 24

Trace form

\( 108 q + 12 q^{4} + 12 q^{6} + 972 q^{9} + O(q^{10}) \) \( 108 q + 12 q^{4} + 12 q^{6} + 972 q^{9} - 76 q^{14} - 316 q^{16} + 228 q^{24} + 348 q^{26} - 216 q^{31} - 128 q^{34} + 108 q^{36} - 624 q^{39} + 472 q^{41} + 1248 q^{44} + 1344 q^{46} - 5292 q^{49} + 108 q^{54} + 2840 q^{56} - 4812 q^{64} + 96 q^{66} + 448 q^{71} + 3928 q^{74} - 1616 q^{76} + 5992 q^{79} + 8748 q^{81} + 2328 q^{84} - 620 q^{86} + 440 q^{89} - 4864 q^{94} + 3972 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)