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

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

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

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