↑

Properties

Label 1.82.a
Level $1$
Weight $82$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 82 \)
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 \(M_{82}(\Gamma_0(1))\).

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

Trace form

\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3} + 44\!\cdots\!52 q^{4} - 18\!\cdots\!00 q^{5} + 79\!\cdots\!32 q^{6} - 31\!\cdots\!00 q^{7} - 54\!\cdots\!20 q^{8} + 11\!\cdots\!98 q^{9} - 66\!\cdots\!00 q^{10}+ \cdots - 63\!\cdots\!24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{82}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.82.a.a 1.a 1.a $6$ $41.550$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 1.82.a.a \(-460872026640\) \(-15\!\cdots\!60\) \(-18\!\cdots\!00\) \(-31\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(-76812004440-\beta _{1})q^{2}+\cdots\)