↑

Properties

Label 27.5.d
Level $27$
Weight $5$
Character orbit 27.d
Rep. character $\chi_{27}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 27.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(27, [\chi])\).

Total New Old
Modular forms 30 10 20
Cusp forms 18 6 12
Eisenstein series 12 4 8

Trace form

\( 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} + O(q^{10}) \) \( 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} - 36 q^{10} - 483 q^{11} - 6 q^{13} + 1146 q^{14} + 15 q^{16} - 258 q^{19} - 1614 q^{20} - 369 q^{22} + 282 q^{23} - 273 q^{25} + 1308 q^{28} + 1056 q^{29} + 1290 q^{31} + 1161 q^{32} + 513 q^{34} + 12 q^{37} + 789 q^{38} - 1314 q^{40} - 7629 q^{41} - 285 q^{43} - 5760 q^{46} + 9642 q^{47} - 1863 q^{49} - 3027 q^{50} - 240 q^{52} + 2016 q^{55} + 462 q^{56} + 6462 q^{58} - 6225 q^{59} + 3630 q^{61} + 15450 q^{64} + 7158 q^{65} - 5055 q^{67} + 10503 q^{68} - 9684 q^{70} - 14622 q^{73} - 26454 q^{74} - 4047 q^{76} - 2580 q^{77} + 4764 q^{79} - 9702 q^{82} + 1866 q^{83} + 12366 q^{85} + 37731 q^{86} + 14787 q^{88} + 34836 q^{91} - 33636 q^{92} - 12708 q^{94} + 13362 q^{95} - 28959 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.5.d.a 27.d 9.d $6$ $2.791$ 6.0.39400128.1 None \(3\) \(0\) \(12\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(4\beta _{1}+2\beta _{2}-\beta _{3}-3\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)