Properties

Label 27.3.b
Level 27
Weight 3
Character orbit b
Rep. character \(\chi_{27}(26,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
27.3.b.a \(1\) \(0.736\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-13\) \(q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots\)
27.3.b.b \(2\) \(0.736\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(10\) \(q+iq^{2}-5q^{4}-iq^{5}+5q^{7}-iq^{8}+\cdots\)