Properties

Label 36.2.a
Level 36
Weight 2
Character orbit a
Rep. character \(\chi_{36}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 36.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(36))\).

Total New Old
Modular forms 12 1 11
Cusp forms 1 1 0
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.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\(q \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 9q^{49} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut -\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\) 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
36.2.a.a \(1\) \(0.287\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(q-4q^{7}+2q^{13}+8q^{19}-5q^{25}-4q^{31}+\cdots\)