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Properties

Label 80.2.n
Level $80$
Weight $2$
Character orbit 80.n
Rep. character $\chi_{80}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).

Total New Old
Modular forms 36 6 30
Cusp forms 12 6 6
Eisenstein series 24 0 24

Trace form

\( 6 q + O(q^{10}) \) \( 6 q - 6 q^{13} - 6 q^{17} - 24 q^{21} - 6 q^{25} + 24 q^{33} + 30 q^{37} + 24 q^{41} + 30 q^{45} - 18 q^{53} - 48 q^{57} - 42 q^{65} - 18 q^{73} + 24 q^{77} + 18 q^{81} - 6 q^{85} - 24 q^{93} - 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.2.n.a 80.n 20.e $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 80.2.n.a \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(2+i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots\)
80.2.n.b 80.n 20.e $4$ $0.639$ \(\Q(\zeta_{12})\) None 80.2.n.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(-1-2\zeta_{12})q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)