Properties

Label 600.3.br
Level $600$
Weight $3$
Character orbit 600.br
Rep. character $\chi_{600}(73,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
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.br (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
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 1984 240 1744
Cusp forms 1856 240 1616
Eisenstein series 128 0 128

Trace form

\( 240 q + 8 q^{5} + 8 q^{7} - 44 q^{13} - 24 q^{15} - 28 q^{17} + 96 q^{23} + 68 q^{25} - 72 q^{33} - 172 q^{37} + 160 q^{41} - 384 q^{43} + 36 q^{45} - 128 q^{47} + 372 q^{53} + 344 q^{55} + 96 q^{57} + 800 q^{59}+ \cdots + 476 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{3}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)