Properties

Label 80.3.p
Level $80$
Weight $3$
Character orbit 80.p
Rep. character $\chi_{80}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $4$
Sturm bound $36$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 80.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(80, [\chi])\).

Total New Old
Modular forms 60 14 46
Cusp forms 36 10 26
Eisenstein series 24 4 20

Trace form

\( 10q + 2q^{3} - 2q^{5} + 2q^{7} + O(q^{10}) \) \( 10q + 2q^{3} - 2q^{5} + 2q^{7} + 4q^{11} - 14q^{13} + 50q^{15} + 2q^{17} + 12q^{21} - 46q^{23} - 14q^{25} - 112q^{27} - 60q^{31} - 68q^{33} - 46q^{35} - 22q^{37} + 12q^{41} + 66q^{43} + 108q^{45} + 242q^{47} + 292q^{51} + 26q^{53} + 148q^{55} - 16q^{57} - 36q^{61} - 222q^{63} + 122q^{65} - 334q^{67} - 412q^{71} + 170q^{73} - 302q^{75} - 100q^{77} + 34q^{81} + 274q^{83} - 142q^{85} + 496q^{87} + 580q^{91} - 116q^{93} + 240q^{95} - 22q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
80.3.p.a \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-6\) \(14\) \(q+(-1+i)q^{3}+(-3+4i)q^{5}+(7+7i)q^{7}+\cdots\)
80.3.p.b \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(10\) \(6\) \(q+(-1+i)q^{3}+5q^{5}+(3+3i)q^{7}+\cdots\)
80.3.p.c \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(-4\) \(q+(2-2i)q^{3}-5iq^{5}+(-2-2i)q^{7}+\cdots\)
80.3.p.d \(4\) \(2.180\) \(\Q(i, \sqrt{41})\) None \(0\) \(2\) \(-6\) \(-14\) \(q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)