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Properties

Label 600.4.bu
Level $600$
Weight $4$
Character orbit 600.bu
Rep. character $\chi_{600}(17,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $720$
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.bu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
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 2944 720 2224
Cusp forms 2816 720 2096
Eisenstein series 128 0 128

Trace form

\( 720 q + 12 q^{7} + O(q^{10}) \) \( 720 q + 12 q^{7} - 24 q^{13} + 12 q^{15} - 72 q^{25} + 168 q^{27} - 204 q^{33} - 576 q^{37} + 2440 q^{39} - 1856 q^{45} + 372 q^{55} + 1720 q^{57} + 5948 q^{63} + 1080 q^{67} + 900 q^{73} - 720 q^{75} - 14232 q^{85} - 1660 q^{87} - 2568 q^{93} + 3408 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)