Properties

Label 144.1.g
Level 144
Weight 1
Character orbit g
Rep. character \(\chi_{144}(127,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 144.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(144, [\chi])\).

Total New Old
Modular forms 13 1 12
Cusp forms 1 1 0
Eisenstein series 12 0 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\(q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(144, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.1.g.a \(1\) \(0.072\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots\)