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Properties

Label 80.3.p
Level $80$
Weight $3$
Character orbit 80.p
Rep. character $\chi_{80}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $4$
Sturm bound $36$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 80.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(80, [\chi])\).

Total New Old
Modular forms 60 14 46
Cusp forms 36 10 26
Eisenstein series 24 4 20

Trace form

\( 10 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + O(q^{10}) \) \( 10 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 4 q^{11} - 14 q^{13} + 50 q^{15} + 2 q^{17} + 12 q^{21} - 46 q^{23} - 14 q^{25} - 112 q^{27} - 60 q^{31} - 68 q^{33} - 46 q^{35} - 22 q^{37} + 12 q^{41} + 66 q^{43} + 108 q^{45} + 242 q^{47} + 292 q^{51} + 26 q^{53} + 148 q^{55} - 16 q^{57} - 36 q^{61} - 222 q^{63} + 122 q^{65} - 334 q^{67} - 412 q^{71} + 170 q^{73} - 302 q^{75} - 100 q^{77} + 34 q^{81} + 274 q^{83} - 142 q^{85} + 496 q^{87} + 580 q^{91} - 116 q^{93} + 240 q^{95} - 22 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.3.p.a 80.p 5.c $2$ $2.180$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-6\) \(14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-3+4i)q^{5}+(7+7i)q^{7}+\cdots\)
80.3.p.b 80.p 5.c $2$ $2.180$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(10\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+5q^{5}+(3+3i)q^{7}+\cdots\)
80.3.p.c 80.p 5.c $2$ $2.180$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}-5iq^{5}+(-2-2i)q^{7}+\cdots\)
80.3.p.d 80.p 5.c $4$ $2.180$ \(\Q(i, \sqrt{41})\) None \(0\) \(2\) \(-6\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)