# Properties

 Label 900.3.bl Level $900$ Weight $3$ Character orbit 900.bl Rep. character $\chi_{900}(79,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $2848$ Sturm bound $540$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.bl (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$900$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$540$$

## Dimensions

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

Total New Old
Modular forms 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

## Trace form

 $$2848q - 5q^{2} - 3q^{4} - 8q^{5} - 14q^{6} - 20q^{8} - 12q^{9} + O(q^{10})$$ $$2848q - 5q^{2} - 3q^{4} - 8q^{5} - 14q^{6} - 20q^{8} - 12q^{9} - 8q^{10} - 10q^{12} - 10q^{13} + 21q^{14} - 3q^{16} - 40q^{17} - 15q^{20} + 42q^{21} - 5q^{22} - 50q^{24} - 8q^{25} - 16q^{26} + 140q^{28} - 6q^{29} + 40q^{30} - 20q^{33} - 11q^{34} - 188q^{36} - 40q^{37} + 625q^{38} - 29q^{40} - 6q^{41} - 530q^{42} + 52q^{44} - 90q^{45} - 28q^{46} + 55q^{48} - 9312q^{49} + 145q^{50} - 5q^{52} - 40q^{53} - 209q^{54} - 150q^{56} - 5q^{58} + 707q^{60} - 6q^{61} - 20q^{62} - 12q^{64} + 44q^{65} - 394q^{66} + 192q^{69} - 246q^{70} - 10q^{72} - 40q^{73} + 194q^{74} - 40q^{76} + 970q^{77} + 1510q^{78} + 930q^{80} + 468q^{81} + 525q^{84} - 58q^{85} - 279q^{86} - 5q^{88} - 24q^{89} + 57q^{90} - 5q^{92} - 199q^{94} + 211q^{96} - 10q^{97} + 510q^{98} + O(q^{100})$$

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

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