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Properties

Label 600.3.i
Level $600$
Weight $3$
Character orbit 600.i
Rep. character $\chi_{600}(149,\cdot)$
Character field $\Q$
Dimension $140$
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.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
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 252 148 104
Cusp forms 228 140 88
Eisenstein series 24 8 16

Trace form

\( 140 q - 10 q^{6} + 4 q^{9} + O(q^{10}) \) \( 140 q - 10 q^{6} + 4 q^{9} + 8 q^{16} + 74 q^{24} - 136 q^{31} - 4 q^{34} - 46 q^{36} - 32 q^{39} - 32 q^{46} - 804 q^{49} - 64 q^{54} + 216 q^{64} + 114 q^{66} - 444 q^{76} + 264 q^{79} + 28 q^{81} + 204 q^{84} - 120 q^{94} - 594 q^{96} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)