Properties

Label 27.7.d
Level $27$
Weight $7$
Character orbit 27.d
Rep. character $\chi_{27}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 7 \)
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: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(27, [\chi])\).

Total New Old
Modular forms 42 14 28
Cusp forms 30 10 20
Eisenstein series 12 4 8

Trace form

\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} + O(q^{10}) \) \( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} - 132 q^{10} - 483 q^{11} - 841 q^{13} - 12174 q^{14} - 1985 q^{16} + 6176 q^{19} + 63186 q^{20} + 3471 q^{22} - 53565 q^{23} + 8452 q^{25} - 22660 q^{28} + 80679 q^{29} - 24601 q^{31} - 218295 q^{32} + 7425 q^{34} + 12764 q^{37} + 371877 q^{38} + 54150 q^{40} - 232251 q^{41} - 93271 q^{43} + 112512 q^{46} + 142887 q^{47} + 86238 q^{49} - 318459 q^{50} + 186920 q^{52} - 419982 q^{55} - 342546 q^{56} - 380658 q^{58} + 995061 q^{59} - 59305 q^{61} + 403066 q^{64} - 1642029 q^{65} + 158513 q^{67} + 1693791 q^{68} - 304788 q^{70} + 933896 q^{73} - 595182 q^{74} + 666641 q^{76} + 2198883 q^{77} + 468707 q^{79} - 2038470 q^{82} - 3008337 q^{83} - 1189944 q^{85} - 1905549 q^{86} - 349773 q^{88} - 211778 q^{91} + 973788 q^{92} + 809124 q^{94} + 2562954 q^{95} + 336029 q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.7.d.a 27.d 9.d $10$ $6.211$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 9.7.d.a \(3\) \(0\) \(219\) \(-121\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-5^{2}\beta _{4}+\beta _{5})q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)