Properties

Label 54.2.a
Level 54
Weight 2
Character orbit a
Rep. character \(\chi_{54}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 18
Trace bound 2

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 54.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(54))\).

Total New Old
Modular forms 15 2 13
Cusp forms 4 2 2
Eisenstein series 11 0 11

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

\(2\)\(3\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2q + 2q^{4} - 2q^{7} + O(q^{10}) \) \( 2q + 2q^{4} - 2q^{7} - 6q^{10} - 8q^{13} + 2q^{16} + 4q^{19} + 6q^{22} + 8q^{25} - 2q^{28} + 10q^{31} + 4q^{37} - 6q^{40} - 20q^{43} + 12q^{46} - 12q^{49} - 8q^{52} - 18q^{55} - 12q^{58} + 16q^{61} + 2q^{64} + 28q^{67} + 6q^{70} - 14q^{73} + 4q^{76} + 16q^{79} + 12q^{82} + 6q^{88} + 8q^{91} - 12q^{94} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(54))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
54.2.a.a \(1\) \(0.431\) \(\Q\) None \(-1\) \(0\) \(3\) \(-1\) \(+\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
54.2.a.b \(1\) \(0.431\) \(\Q\) None \(1\) \(0\) \(-3\) \(-1\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(54))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(54)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)