Properties

Label 600.4.bq
Level $600$
Weight $4$
Character orbit 600.bq
Rep. character $\chi_{600}(67,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
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.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2912 1440 1472
Cusp forms 2848 1440 1408
Eisenstein series 64 0 64

Trace form

\( 1440 q - 84 q^{8} + O(q^{10}) \) \( 1440 q - 84 q^{8} + 72 q^{10} - 24 q^{12} + 104 q^{17} - 380 q^{20} - 44 q^{22} + 88 q^{25} + 1068 q^{28} - 408 q^{30} - 340 q^{32} - 912 q^{35} + 5020 q^{38} - 3148 q^{40} + 660 q^{42} - 864 q^{43} + 2660 q^{44} - 528 q^{48} - 8476 q^{50} + 5196 q^{52} + 2216 q^{58} - 420 q^{60} + 8092 q^{62} - 9660 q^{64} + 1048 q^{65} - 3696 q^{67} + 1464 q^{68} - 204 q^{70} + 756 q^{72} - 1480 q^{73} + 72 q^{78} + 1684 q^{80} + 29160 q^{81} - 1568 q^{82} + 5360 q^{83} - 11280 q^{84} - 3556 q^{88} + 2200 q^{89} + 432 q^{90} + 168 q^{92} + 2760 q^{94} - 1740 q^{96} + 7768 q^{97} + 19584 q^{98} + O(q^{100}) \)

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

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