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Properties

Label 600.3.bv
Level $600$
Weight $3$
Character orbit 600.bv
Rep. character $\chi_{600}(83,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1888$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 600.bv (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 600 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(600, [\chi])\).

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 16 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{9} + O(q^{10}) \) \( 1888 q - 16 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{9} - 24 q^{10} - 26 q^{12} - 12 q^{16} - 14 q^{18} - 40 q^{19} + 24 q^{22} - 32 q^{25} - 16 q^{27} + 32 q^{28} + 22 q^{30} - 52 q^{33} - 20 q^{34} - 70 q^{36} + 52 q^{40} - 614 q^{42} + 96 q^{43} - 12 q^{46} + 268 q^{48} - 32 q^{51} + 84 q^{52} + 640 q^{54} - 52 q^{57} - 184 q^{58} - 886 q^{60} - 20 q^{64} - 150 q^{66} - 32 q^{67} - 288 q^{70} + 70 q^{72} - 32 q^{73} + 208 q^{75} - 160 q^{76} - 264 q^{78} - 12 q^{81} + 436 q^{82} - 10 q^{84} + 840 q^{88} - 462 q^{90} - 24 q^{91} + 1380 q^{94} - 6 q^{96} + 96 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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