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Properties

Label 600.3.bj
Level $600$
Weight $3$
Character orbit 600.bj
Rep. character $\chi_{600}(221,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $944$
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.bj (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 600 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 976 976 0
Cusp forms 944 944 0
Eisenstein series 32 32 0

Trace form

\( 944 q - 6 q^{4} + 5 q^{6} - 32 q^{7} - 6 q^{9} + O(q^{10}) \) \( 944 q - 6 q^{4} + 5 q^{6} - 32 q^{7} - 6 q^{9} + 4 q^{10} - 21 q^{12} + 10 q^{15} + 54 q^{16} - 30 q^{18} - 46 q^{22} + 80 q^{24} - 16 q^{25} - 86 q^{28} + 67 q^{30} - 12 q^{31} + 30 q^{33} + 58 q^{34} + 179 q^{36} - 42 q^{39} - 68 q^{40} + 125 q^{42} - 122 q^{46} + 94 q^{48} + 5904 q^{49} - 384 q^{52} - 190 q^{54} + 212 q^{55} - 52 q^{57} + 150 q^{58} + 16 q^{60} - 300 q^{63} - 126 q^{64} + 268 q^{66} - 456 q^{70} - 181 q^{72} - 12 q^{73} + 160 q^{76} - 501 q^{78} - 12 q^{79} - 6 q^{81} + 588 q^{82} - 390 q^{84} - 418 q^{87} + 590 q^{88} - 48 q^{90} + 388 q^{94} + 160 q^{96} - 60 q^{97} + O(q^{100}) \)

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.