↑

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 $540$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

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