Properties

Label 27.4.a
Level 27
Weight 4
Character orbit a
Rep. character \(\chi_{27}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(27))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
27.4.a.a \(1\) \(1.593\) \(\Q\) None \(-3\) \(0\) \(-15\) \(-25\) \(-\) \(q-3q^{2}+q^{4}-15q^{5}-5^{2}q^{7}+21q^{8}+\cdots\)
27.4.a.b \(1\) \(1.593\) \(\Q\) None \(3\) \(0\) \(15\) \(-25\) \(+\) \(q+3q^{2}+q^{4}+15q^{5}-5^{2}q^{7}-21q^{8}+\cdots\)
27.4.a.c \(2\) \(1.593\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(22\) \(+\) \(q+\beta q^{2}+10q^{4}-4\beta q^{5}+11q^{7}+2\beta q^{8}+\cdots\)

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

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