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Properties

Label 1.72.a
Level $1$
Weight $72$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 72 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{72}(\Gamma_0(1))\).

Total New Old
Modular forms 7 7 0
Cusp forms 6 6 0
Eisenstein series 1 1 0

Trace form

\( 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3} + 82\!\cdots\!68 q^{4} - 42\!\cdots\!20 q^{5} - 38\!\cdots\!88 q^{6} + 33\!\cdots\!00 q^{7} + 26\!\cdots\!80 q^{8} + 28\!\cdots\!42 q^{9} - 26\!\cdots\!20 q^{10}+ \cdots - 14\!\cdots\!96 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{72}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.72.a.a 1.a 1.a $6$ $31.925$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 1.72.a.a \(66157336440\) \(89\!\cdots\!40\) \(-42\!\cdots\!20\) \(33\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(11026222740-\beta _{1})q^{2}+(14982825462961740+\cdots)q^{3}+\cdots\)