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

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

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