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Properties

Label 600.3.n
Level $600$
Weight $3$
Character orbit 600.n
Rep. character $\chi_{600}(101,\cdot)$
Character field $\Q$
Dimension $146$
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.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 252 158 94
Cusp forms 228 146 82
Eisenstein series 24 12 12

Trace form

\( 146 q + 4 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{9} + O(q^{10}) \) \( 146 q + 4 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{9} + 12 q^{12} - 32 q^{16} + 36 q^{18} + 28 q^{22} - 18 q^{24} - 44 q^{28} - 76 q^{31} + 28 q^{33} + 60 q^{34} - 114 q^{36} + 152 q^{39} + 96 q^{42} - 40 q^{46} - 4 q^{48} + 790 q^{49} - 136 q^{52} + 144 q^{54} + 24 q^{57} + 68 q^{58} - 60 q^{63} - 176 q^{64} - 70 q^{66} - 288 q^{72} + 84 q^{73} - 20 q^{76} + 152 q^{78} + 132 q^{79} + 66 q^{81} - 296 q^{82} - 532 q^{84} - 12 q^{87} - 140 q^{88} - 432 q^{94} - 194 q^{96} + 132 q^{97} + O(q^{100}) \)

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.

Decomposition of \(S_{3}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)