Properties

 Label 55.17.d Level $55$ Weight $17$ Character orbit 55.d Rep. character $\chi_{55}(54,\cdot)$ Character field $\Q$ Dimension $94$ Newform subspaces $5$ Sturm bound $102$ Trace bound $4$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$55 = 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$17$$ Character orbit: $$[\chi]$$ $$=$$ 55.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$102$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{17}(55, [\chi])$$.

Total New Old
Modular forms 98 98 0
Cusp forms 94 94 0
Eisenstein series 4 4 0

Trace form

 $$94 q + 3014652 q^{4} - 330461 q^{5} - 1262640952 q^{9} + O(q^{10})$$ $$94 q + 3014652 q^{4} - 330461 q^{5} - 1262640952 q^{9} + 94771882 q^{11} + 606959656 q^{14} - 4851561495 q^{15} + 73505406040 q^{16} - 108097278504 q^{20} + 102230886901 q^{25} - 47745195404 q^{26} + 2987126328674 q^{31} + 282271475496 q^{34} - 30977307859472 q^{36} - 5256689206356 q^{44} - 9089329392566 q^{45} + 326081385770382 q^{49} + 35664610472021 q^{55} + 106477132145672 q^{56} - 421624558021438 q^{59} + 164768214118320 q^{60} + 3115856446239348 q^{64} - 1055691766016940 q^{66} - 712248217441446 q^{69} + 372393282252900 q^{70} - 1625286603116122 q^{71} + 1586187021843285 q^{75} - 15696795506808256 q^{80} + 23023311507405110 q^{81} - 1339130989661204 q^{86} - 13226028506679382 q^{89} - 5259060274394664 q^{91} - 41923561217430044 q^{99} + O(q^{100})$$

Decomposition of $$S_{17}^{\mathrm{new}}(55, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.17.d.a $1$ $89.278$ $$\Q$$ $$\Q(\sqrt{-55})$$ $$-17$$ $$0$$ $$390625$$ $$9886078$$ $$q-17q^{2}-65247q^{4}+5^{8}q^{5}+9886078q^{7}+\cdots$$
55.17.d.b $1$ $89.278$ $$\Q$$ $$\Q(\sqrt{-55})$$ $$17$$ $$0$$ $$390625$$ $$-9886078$$ $$q+17q^{2}-65247q^{4}+5^{8}q^{5}-9886078q^{7}+\cdots$$
55.17.d.c $2$ $89.278$ $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$-543551$$ $$0$$ $$q+(-565-1130\beta )q^{3}-2^{16}q^{4}+(-283861+\cdots)q^{5}+\cdots$$
55.17.d.d $2$ $89.278$ $$\Q(\sqrt{55})$$ $$\Q(\sqrt{-55})$$ $$0$$ $$0$$ $$-781250$$ $$0$$ $$q+23\beta q^{2}+196319q^{4}-5^{8}q^{5}-266656\beta q^{7}+\cdots$$
55.17.d.e $88$ $89.278$ None $$0$$ $$0$$ $$213090$$ $$0$$