Properties

Label 72.2.a
Level $72$
Weight $2$
Character orbit 72.a
Rep. character $\chi_{72}(1,\cdot)$
Character field $\Q$
Dimension $1$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(72))\).

Total New Old
Modular forms 20 1 19
Cusp forms 5 1 4
Eisenstein series 15 0 15

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

\( q + 2 q^{5} + O(q^{10}) \) \( q + 2 q^{5} - 4 q^{11} - 2 q^{13} - 2 q^{17} - 4 q^{19} + 8 q^{23} - q^{25} - 6 q^{29} + 8 q^{31} + 6 q^{37} + 6 q^{41} + 4 q^{43} - 7 q^{49} + 2 q^{53} - 8 q^{55} - 4 q^{59} - 2 q^{61} - 4 q^{65} - 4 q^{67} - 8 q^{71} + 10 q^{73} - 8 q^{79} + 4 q^{83} - 4 q^{85} + 6 q^{89} - 8 q^{95} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(72))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
72.2.a.a 72.a 1.a $1$ $0.575$ \(\Q\) None 24.2.a.a \(0\) \(0\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(72))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(72)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)