Properties

Label 80.5.p
Level $80$
Weight $5$
Character orbit 80.p
Rep. character $\chi_{80}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $22$
Newform subspaces $7$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 80.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 7 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(80, [\chi])\).

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 4 q^{11} - 122 q^{13} - 670 q^{15} - 122 q^{17} - 612 q^{21} + 1442 q^{23} + 166 q^{25} - 1120 q^{27} - 124 q^{31} + 1276 q^{33} + 2594 q^{35} + 1398 q^{37} - 1252 q^{41}+ \cdots - 7722 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.5.p.a 80.p 5.c $2$ $8.270$ \(\Q(\sqrt{-1}) \) None 40.5.l.a \(0\) \(-20\) \(40\) \(84\) $\mathrm{SU}(2)[C_{4}]$ \(q+(10 i-10)q^{3}+(15 i+20)q^{5}+\cdots\)
80.5.p.b 80.p 5.c $2$ $8.270$ \(\Q(\sqrt{-1}) \) None 10.5.c.a \(0\) \(-18\) \(-30\) \(-58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(9 i-9)q^{3}+(20 i-15)q^{5}+(-29 i-29)q^{7}+\cdots\)
80.5.p.c 80.p 5.c $2$ $8.270$ \(\Q(\sqrt{-1}) \) None 10.5.c.b \(0\) \(-2\) \(-30\) \(38\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i-1)q^{3}+(-20 i-15)q^{5}+(19 i+19)q^{7}+\cdots\)
80.5.p.d 80.p 5.c $2$ $8.270$ \(\Q(\sqrt{-1}) \) None 5.5.c.a \(0\) \(12\) \(40\) \(52\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-6 i+6)q^{3}+(15 i+20)q^{5}+\cdots\)
80.5.p.e 80.p 5.c $4$ $8.270$ \(\Q(i, \sqrt{241})\) None 20.5.f.a \(0\) \(10\) \(-6\) \(-110\) $\mathrm{SU}(2)[C_{4}]$ \(q+(3-3\beta _{1}+\beta _{3})q^{3}+(-3-3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
80.5.p.f 80.p 5.c $4$ $8.270$ \(\Q(i, \sqrt{29})\) None 40.5.l.b \(0\) \(12\) \(-12\) \(-44\) $\mathrm{SU}(2)[C_{4}]$ \(q+(3-3\beta _{1})q^{3}+(-3-6\beta _{1}-\beta _{3})q^{5}+\cdots\)
80.5.p.g 80.p 5.c $6$ $8.270$ 6.0.313431616.3 None 40.5.l.c \(0\) \(8\) \(-4\) \(40\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}+\beta _{3})q^{3}+(-1+7\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)