Properties

Label 72.2.f
Level $72$
Weight $2$
Character orbit 72.f
Rep. character $\chi_{72}(35,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

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

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