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 $4$

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