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Properties

Label 900.4.z
Level $900$
Weight $4$
Character orbit 900.z
Rep. character $\chi_{900}(179,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $720$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 900.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

Total New Old
Modular forms 2192 720 1472
Cusp forms 2128 720 1408
Eisenstein series 64 0 64

Trace form

\( 720 q + O(q^{10}) \) \( 720 q + 72 q^{10} - 216 q^{16} - 168 q^{25} - 288 q^{34} - 660 q^{37} + 12 q^{40} + 840 q^{46} + 36096 q^{49} + 300 q^{52} + 6840 q^{58} + 312 q^{61} + 1872 q^{64} + 1896 q^{70} - 1224 q^{76} + 3072 q^{85} - 3960 q^{88} - 204 q^{94} - 18600 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)