Properties

Label 135.2.a
Level 135
Weight 2
Character orbit a
Rep. character \(\chi_{135}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 4
Sturm bound 36
Trace bound 2

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Defining parameters

Level: \( N \) = \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 135.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(135))\).

Total New Old
Modular forms 24 6 18
Cusp forms 13 6 7
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.

\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(5\)

Trace form

\( 6q + 10q^{4} - 2q^{7} + O(q^{10}) \) \( 6q + 10q^{4} - 2q^{7} + 2q^{10} + 2q^{13} - 14q^{16} + 2q^{19} - 20q^{22} + 6q^{25} - 32q^{28} - 8q^{31} + 10q^{34} + 18q^{37} - 12q^{40} - 4q^{43} - 18q^{46} + 32q^{49} + 24q^{52} + 8q^{55} + 8q^{58} + 26q^{61} - 24q^{64} - 50q^{67} + 12q^{70} + 26q^{73} + 30q^{76} - 38q^{79} + 68q^{82} + 8q^{85} - 12q^{88} - 10q^{91} + 40q^{94} + 6q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(135))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5
135.2.a.a \(1\) \(1.078\) \(\Q\) None \(-2\) \(0\) \(-1\) \(-3\) \(+\) \(+\) \(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
135.2.a.b \(1\) \(1.078\) \(\Q\) None \(2\) \(0\) \(1\) \(-3\) \(+\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
135.2.a.c \(2\) \(1.078\) \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(2\) \(2\) \(+\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots\)
135.2.a.d \(2\) \(1.078\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+(2-2\beta )q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(135))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(135)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)