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Properties

Label 27.3.b
Level $27$
Weight $3$
Character orbit 27.b
Rep. character $\chi_{27}(26,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $9$
Trace bound $1$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(27, [\chi])\).

Total New Old
Modular forms 9 3 6
Cusp forms 3 3 0
Eisenstein series 6 0 6

Trace form

\( 3 q - 6 q^{4} - 3 q^{7} + O(q^{10}) \) \( 3 q - 6 q^{4} - 3 q^{7} + 18 q^{10} - 21 q^{13} - 6 q^{16} - 21 q^{19} + 90 q^{22} + 57 q^{25} - 102 q^{28} - 48 q^{31} - 108 q^{34} + 87 q^{37} - 18 q^{40} + 78 q^{43} + 72 q^{46} + 72 q^{49} + 96 q^{52} - 90 q^{55} - 180 q^{58} - 273 q^{61} + 246 q^{64} - 129 q^{67} + 90 q^{70} + 33 q^{73} + 204 q^{76} + 159 q^{79} - 360 q^{82} + 108 q^{85} - 90 q^{88} - 87 q^{91} + 36 q^{94} - 3 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.3.b.a 27.b 3.b $1$ $0.736$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-13\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots\)
27.3.b.b 27.b 3.b $2$ $0.736$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-5q^{4}-iq^{5}+5q^{7}-iq^{8}+\cdots\)