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Properties

Label 27.6.c
Level $27$
Weight $6$
Character orbit 27.c
Rep. character $\chi_{27}(10,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 27.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(27, [\chi])\).

Total New Old
Modular forms 36 12 24
Cusp forms 24 8 16
Eisenstein series 12 4 8

Trace form

\( 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8} + O(q^{10}) \) \( 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8} + 60 q^{10} - 444 q^{11} - 182 q^{13} - 1392 q^{14} - 289 q^{16} + 4356 q^{17} + 952 q^{19} - 6684 q^{20} + 1011 q^{22} - 8844 q^{23} - 1654 q^{25} + 24888 q^{26} - 1604 q^{28} - 12018 q^{29} + 1132 q^{31} - 8703 q^{32} + 10125 q^{34} + 16224 q^{35} - 15176 q^{37} + 11145 q^{38} - 8736 q^{40} - 1248 q^{41} - 6092 q^{43} - 49530 q^{44} + 45960 q^{46} + 60 q^{47} + 9090 q^{49} + 57057 q^{50} - 32510 q^{52} - 20952 q^{53} - 36120 q^{55} + 61170 q^{56} + 8328 q^{58} - 2076 q^{59} + 48142 q^{61} - 241764 q^{62} - 20926 q^{64} + 13146 q^{65} - 7148 q^{67} + 123129 q^{68} - 654 q^{70} + 71856 q^{71} + 122452 q^{73} + 160320 q^{74} - 49571 q^{76} - 39534 q^{77} - 59516 q^{79} - 124512 q^{80} - 233598 q^{82} - 117696 q^{83} + 28836 q^{85} + 15915 q^{86} + 104523 q^{88} + 451728 q^{89} + 111392 q^{91} - 134034 q^{92} + 169464 q^{94} - 294888 q^{95} + 33976 q^{97} - 57654 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.6.c.a 27.c 9.c $8$ $4.330$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-3\) \(0\) \(-78\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(-13\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)