Properties

Label 900.3.bb
Level $900$
Weight $3$
Character orbit 900.bb
Rep. character $\chi_{900}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $592$
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.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1472 608 864
Cusp forms 1408 592 816
Eisenstein series 64 16 48

Trace form

\( 592q + 5q^{2} - 3q^{4} + 10q^{5} + 20q^{8} + O(q^{10}) \) \( 592q + 5q^{2} - 3q^{4} + 10q^{5} + 20q^{8} - 13q^{10} - 10q^{13} - 15q^{14} - 63q^{16} + 10q^{17} - 7q^{20} + 70q^{22} - 30q^{25} + 66q^{26} - 85q^{28} - 14q^{29} + 69q^{34} - 20q^{37} + 155q^{38} - 210q^{40} - 94q^{41} - 70q^{44} - 95q^{46} + 3712q^{49} + 463q^{50} + 480q^{52} + 80q^{53} + 60q^{56} + 370q^{58} + 14q^{61} + 330q^{62} + 12q^{64} + 140q^{65} - 418q^{70} - 10q^{73} - 304q^{74} + 80q^{76} + 500q^{77} - 82q^{80} - 40q^{85} + 165q^{86} - 170q^{88} - 384q^{89} + 940q^{92} + 325q^{94} + 190q^{97} + 340q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)