Properties

Label 80.2.q
Level $80$
Weight $2$
Character orbit 80.q
Rep. character $\chi_{80}(29,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $3$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(2\)
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

\( 20q - 4q^{4} - 2q^{5} - 4q^{6} + O(q^{10}) \) \( 20q - 4q^{4} - 2q^{5} - 4q^{6} - 8q^{10} - 4q^{11} - 4q^{14} - 4q^{15} - 12q^{19} - 16q^{20} - 16q^{21} - 16q^{24} + 32q^{26} - 4q^{29} - 24q^{30} + 16q^{31} + 32q^{34} - 24q^{35} + 68q^{36} + 24q^{40} + 16q^{44} + 14q^{45} + 4q^{46} - 12q^{49} + 36q^{50} + 8q^{54} - 56q^{56} + 12q^{59} + 48q^{60} - 20q^{61} - 16q^{64} - 12q^{65} - 96q^{66} + 20q^{70} - 24q^{74} + 36q^{75} - 96q^{76} + 48q^{79} - 8q^{80} + 4q^{81} - 80q^{84} + 8q^{85} - 52q^{86} - 84q^{90} - 16q^{91} + 4q^{94} + 20q^{95} + 56q^{96} + 76q^{99} + O(q^{100}) \)

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.q.a \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None \(-2\) \(2\) \(2\) \(0\) \(q+(-1-i)q^{2}+(1+i)q^{3}+2iq^{4}+\cdots\)
80.2.q.b \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None \(2\) \(-2\) \(4\) \(0\) \(q+(1+i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots\)
80.2.q.c \(16\) \(0.639\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)