Properties

Label 900.3.bh
Level $900$
Weight $3$
Character orbit 900.bh
Rep. character $\chi_{900}(287,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 2944 960 1984
Cusp forms 2816 960 1856
Eisenstein series 128 0 128

Trace form

\( 960q + O(q^{10}) \) \( 960q - 16q^{10} - 112q^{22} - 32q^{28} - 16q^{37} + 216q^{40} + 488q^{52} + 400q^{58} - 464q^{70} + 224q^{73} + 400q^{82} - 448q^{85} + 2096q^{88} + 400q^{94} - 640q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)