Properties

Label 72.2.f
Level 72
Weight 2
Character orbit f
Rep. character \(\chi_{72}(35,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 72.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(72, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\(4q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 24q^{28} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 20q^{49} \) \(\mathstrut -\mathstrut 24q^{52} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 32q^{64} \) \(\mathstrut -\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 4q^{82} \) \(\mathstrut +\mathstrut 32q^{88} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut +\mathstrut 32q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
72.2.f.a \(4\) \(0.575\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)