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Properties

Label 80.2.s
Level $80$
Weight $2$
Character orbit 80.s
Rep. character $\chi_{80}(3,\cdot)$
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.s (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

\( 20 q - 2 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 8 q^{8} + 12 q^{9} + O(q^{10}) \) \( 20 q - 2 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 8 q^{8} + 12 q^{9} + 2 q^{10} - 4 q^{11} - 12 q^{15} - 8 q^{16} - 4 q^{17} - 26 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{21} + 12 q^{22} - 4 q^{23} - 12 q^{24} - 20 q^{26} - 16 q^{27} + 28 q^{28} + 36 q^{30} + 28 q^{32} - 4 q^{33} + 24 q^{34} + 20 q^{35} - 4 q^{36} + 24 q^{38} + 32 q^{40} - 16 q^{42} - 40 q^{44} - 18 q^{45} + 12 q^{46} + 24 q^{47} + 20 q^{48} - 6 q^{50} + 4 q^{51} + 16 q^{52} - 4 q^{53} - 4 q^{54} - 4 q^{55} + 20 q^{56} - 12 q^{57} + 48 q^{58} + 16 q^{59} + 12 q^{61} - 36 q^{62} - 12 q^{63} + 16 q^{64} - 4 q^{65} + 4 q^{66} - 56 q^{68} - 28 q^{69} - 52 q^{70} + 24 q^{71} - 64 q^{72} - 8 q^{73} - 36 q^{74} + 4 q^{75} - 4 q^{76} - 32 q^{77} - 28 q^{78} - 76 q^{80} - 20 q^{81} + 40 q^{82} + 36 q^{83} + 48 q^{84} + 8 q^{85} - 28 q^{86} + 52 q^{87} - 16 q^{88} - 6 q^{90} + 12 q^{91} - 4 q^{92} - 28 q^{94} + 40 q^{95} - 56 q^{96} - 4 q^{97} - 78 q^{98} + 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.2.s.a 80.s 80.s $2$ $0.639$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
80.2.s.b 80.s 80.s $18$ $0.639$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots\)