Properties

Label 27.9.d
Level $27$
Weight $9$
Character orbit 27.d
Rep. character $\chi_{27}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $1$
Sturm bound $27$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
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: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(27, [\chi])\).

Total New Old
Modular forms 54 18 36
Cusp forms 42 14 28
Eisenstein series 12 4 8

Trace form

\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} + O(q^{10}) \) \( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} - 516 q^{10} + 28677 q^{11} + 1684 q^{13} - 120966 q^{14} - 65281 q^{16} - 269630 q^{19} - 539454 q^{20} + 61311 q^{22} + 1000452 q^{23} + 65177 q^{25} + 1075708 q^{28} - 3797682 q^{29} - 164132 q^{31} + 8461881 q^{32} + 654993 q^{34} - 1671668 q^{37} - 10967691 q^{38} + 613326 q^{40} + 10239447 q^{41} + 791815 q^{43} + 1189536 q^{46} - 31148628 q^{47} - 4826637 q^{49} + 63849453 q^{50} - 5552720 q^{52} + 8107476 q^{55} - 116638674 q^{56} + 14211822 q^{58} + 83493795 q^{59} - 5255600 q^{61} - 26813830 q^{64} - 69232992 q^{65} - 8288855 q^{67} + 77746743 q^{68} + 27813756 q^{70} - 36721682 q^{73} + 10383450 q^{74} - 42822959 q^{76} - 56158710 q^{77} - 32771822 q^{79} + 236099418 q^{82} + 198915996 q^{83} + 97486146 q^{85} - 146190669 q^{86} + 24955827 q^{88} - 201514504 q^{91} + 295365804 q^{92} - 36698244 q^{94} - 386813838 q^{95} + 127049161 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.9.d.a 27.d 9.d $14$ $10.999$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(0\) \(-438\) \(922\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-2\beta _{1}-2\beta _{2}+110\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

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