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Properties

Label 80.2.j
Level $80$
Weight $2$
Character orbit 80.j
Rep. character $\chi_{80}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 8 q^{8} - 12 q^{9} + O(q^{10}) \) \( 20 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 8 q^{8} - 12 q^{9} - 6 q^{10} - 4 q^{11} + 12 q^{12} - 4 q^{13} + 12 q^{15} - 8 q^{16} - 4 q^{17} + 14 q^{18} + 8 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{23} + 12 q^{24} - 20 q^{26} - 16 q^{28} + 16 q^{30} - 12 q^{32} - 4 q^{33} - 24 q^{34} - 4 q^{36} - 4 q^{37} + 28 q^{38} + 24 q^{40} + 28 q^{42} - 36 q^{43} + 40 q^{44} - 6 q^{45} + 12 q^{46} - 24 q^{47} + 60 q^{48} + 22 q^{50} + 4 q^{51} - 40 q^{52} + 4 q^{54} - 4 q^{55} + 20 q^{56} + 12 q^{57} - 20 q^{58} - 16 q^{59} - 60 q^{60} + 12 q^{61} + 4 q^{62} + 12 q^{63} - 16 q^{64} - 4 q^{65} + 4 q^{66} + 20 q^{67} + 40 q^{68} + 28 q^{69} - 48 q^{70} + 24 q^{71} - 32 q^{72} + 8 q^{73} + 36 q^{74} + 48 q^{75} - 4 q^{76} - 92 q^{78} - 28 q^{80} - 20 q^{81} - 36 q^{82} - 48 q^{84} - 12 q^{85} - 28 q^{86} + 52 q^{87} - 96 q^{88} - 70 q^{90} + 12 q^{91} + 56 q^{92} + 8 q^{93} + 28 q^{94} - 40 q^{95} - 56 q^{96} - 4 q^{97} + 54 q^{98} - 20 q^{99} + O(q^{100}) \)

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.j.a 80.j 80.j $2$ $0.639$ \(\Q(\sqrt{-1}) \) None 80.2.j.a \(2\) \(0\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+2iq^{3}-2iq^{4}+(1+2i)q^{5}+\cdots\)
80.2.j.b 80.j 80.j $18$ $0.639$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 80.2.j.b \(-4\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{2}-\beta _{16}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots\)