Properties

Label 27.4.a
Level $27$
Weight $4$
Character orbit 27.a
Rep. character $\chi_{27}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $12$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 27.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(27))\).

Total New Old
Modular forms 12 4 8
Cusp forms 6 4 2
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)Dim.
\(+\)\(3\)
\(-\)\(1\)

Trace form

\( 4 q + 22 q^{4} - 28 q^{7} + O(q^{10}) \) \( 4 q + 22 q^{4} - 28 q^{7} - 54 q^{10} + 98 q^{13} - 230 q^{16} + 62 q^{19} + 54 q^{22} + 526 q^{25} + 170 q^{28} - 334 q^{31} - 694 q^{37} - 918 q^{40} - 244 q^{43} + 1404 q^{46} + 120 q^{49} + 620 q^{52} - 1026 q^{55} + 2484 q^{58} + 782 q^{61} - 590 q^{64} - 1522 q^{67} - 3834 q^{70} + 1844 q^{73} + 584 q^{76} + 26 q^{79} - 2484 q^{82} + 3888 q^{85} + 918 q^{88} - 362 q^{91} - 5292 q^{94} - 568 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(27))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3
27.4.a.a 27.a 1.a $1$ $1.593$ \(\Q\) None \(-3\) \(0\) \(-15\) \(-25\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}-15q^{5}-5^{2}q^{7}+21q^{8}+\cdots\)
27.4.a.b 27.a 1.a $1$ $1.593$ \(\Q\) None \(3\) \(0\) \(15\) \(-25\) $+$ $\mathrm{SU}(2)$ \(q+3q^{2}+q^{4}+15q^{5}-5^{2}q^{7}-21q^{8}+\cdots\)
27.4.a.c 27.a 1.a $2$ $1.593$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(22\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+10q^{4}-4\beta q^{5}+11q^{7}+2\beta q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(27))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(27)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)