Properties

Label 900.6.z
Level $900$
Weight $6$
Character orbit 900.z
Rep. character $\chi_{900}(179,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1200$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

Total New Old
Modular forms 3632 1200 2432
Cusp forms 3568 1200 2368
Eisenstein series 64 0 64

Trace form

\( 1200 q + O(q^{10}) \) \( 1200 q - 568 q^{10} + 7656 q^{16} + 2728 q^{25} - 24608 q^{34} + 18820 q^{37} + 13324 q^{40} + 28360 q^{46} + 2844416 q^{49} + 253900 q^{52} - 382920 q^{58} - 36632 q^{61} + 3792 q^{64} + 100360 q^{70} + 16824 q^{76} - 168960 q^{85} + 1147080 q^{88} + 113236 q^{94} + 1652200 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)