Properties

Label 80.2.l
Level $80$
Weight $2$
Character orbit 80.l
Rep. character $\chi_{80}(21,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

Trace form

\( 16q - 4q^{4} - 12q^{6} + O(q^{10}) \) \( 16q - 4q^{4} - 12q^{6} + 4q^{10} - 8q^{11} - 12q^{12} + 4q^{14} - 8q^{15} + 16q^{16} - 8q^{19} + 8q^{20} - 20q^{22} + 8q^{24} - 16q^{26} + 24q^{27} - 4q^{28} - 16q^{29} + 16q^{34} - 4q^{36} - 16q^{37} + 20q^{38} + 60q^{42} + 8q^{43} + 40q^{44} - 4q^{46} - 40q^{47} - 40q^{48} - 16q^{49} - 4q^{50} - 32q^{51} + 56q^{52} + 16q^{53} + 32q^{54} + 16q^{56} - 12q^{58} - 8q^{59} - 28q^{60} + 16q^{61} - 8q^{62} + 40q^{63} - 16q^{64} + 40q^{67} - 48q^{68} + 16q^{69} - 8q^{70} - 40q^{72} - 72q^{74} + 16q^{77} - 16q^{78} + 16q^{79} + 16q^{80} - 16q^{81} - 76q^{82} + 40q^{83} - 64q^{84} - 16q^{85} + 28q^{86} + 36q^{90} + 32q^{91} - 52q^{92} - 48q^{93} - 36q^{94} + 32q^{95} + 8q^{96} + 60q^{98} - 8q^{99} + O(q^{100}) \)

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.l.a \(16\) \(0.639\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}+(\beta _{3}-\beta _{6}+\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)