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Properties

Label 600.4.be
Level $600$
Weight $4$
Character orbit 600.be
Rep. character $\chi_{600}(109,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $720$
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.be (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1456 720 736
Cusp forms 1424 720 704
Eisenstein series 32 0 32

Trace form

\( 720 q + 210 q^{8} - 1620 q^{9} + O(q^{10}) \) \( 720 q + 210 q^{8} - 1620 q^{9} - 42 q^{10} + 132 q^{14} + 108 q^{16} - 364 q^{20} - 650 q^{22} - 44 q^{25} - 20 q^{26} - 876 q^{30} - 744 q^{31} + 144 q^{34} - 2490 q^{38} - 624 q^{39} + 2860 q^{40} + 472 q^{41} - 798 q^{44} + 420 q^{46} - 35280 q^{49} + 3476 q^{50} - 4020 q^{52} + 144 q^{55} + 1116 q^{56} - 5030 q^{58} - 402 q^{60} - 5350 q^{62} + 1962 q^{64} + 5404 q^{65} - 1272 q^{66} + 1024 q^{70} - 1890 q^{72} + 2156 q^{74} - 3592 q^{76} + 3160 q^{79} + 1644 q^{80} - 14580 q^{81} - 3384 q^{84} - 3660 q^{86} - 1210 q^{88} - 660 q^{89} - 108 q^{90} - 2630 q^{92} - 3770 q^{94} - 8824 q^{95} - 4740 q^{96} - 3720 q^{97} + 13580 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)