Properties

Label 72.1.p
Level 72
Weight 1
Character orbit p
Rep. character \(\chi_{72}(43,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 72.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(72, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{24} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut -\mathstrut q^{36} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut -\mathstrut q^{54} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut +\mathstrut q^{76} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut q^{86} \) \(\mathstrut +\mathstrut q^{88} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(72, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
72.1.p.a \(2\) \(0.036\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)