Properties

Label 55.6.e
Level $55$
Weight $6$
Character orbit 55.e
Rep. character $\chi_{55}(32,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 55.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(55, [\chi])\).

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

Trace form

\( 56 q - 6 q^{3} - 48 q^{5} + O(q^{10}) \) \( 56 q - 6 q^{3} - 48 q^{5} - 364 q^{11} + 2808 q^{12} + 1116 q^{15} - 10512 q^{16} + 14624 q^{20} + 2680 q^{22} - 2106 q^{23} - 6246 q^{25} + 2432 q^{26} + 4326 q^{27} + 9672 q^{31} + 27914 q^{33} - 117672 q^{36} + 21618 q^{37} + 4400 q^{38} - 43480 q^{42} + 22718 q^{45} + 5268 q^{47} + 89904 q^{48} + 5984 q^{53} - 18106 q^{55} + 304264 q^{56} - 220200 q^{58} - 173264 q^{60} + 207000 q^{66} - 163722 q^{67} - 216880 q^{70} + 20612 q^{71} + 203556 q^{75} - 341160 q^{77} + 15160 q^{78} + 616192 q^{80} - 203292 q^{81} + 349720 q^{82} - 94768 q^{86} + 539000 q^{88} - 864768 q^{91} + 179288 q^{92} - 33002 q^{93} - 306762 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.6.e.a 55.e 55.e $4$ $8.821$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(-62\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-15+\beta _{1}-2^{4}\beta _{2}+\beta _{3})q^{3}-2^{5}\beta _{2}q^{4}+\cdots\)
55.6.e.b 55.e 55.e $52$ $8.821$ None \(0\) \(56\) \(-48\) \(0\) $\mathrm{SU}(2)[C_{4}]$