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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
80.2.s.a \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(-4\) \(-6\) \(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
80.2.s.b \(18\) \(0.639\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(2\) \(2\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots\)