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Properties

Label 80.2.c
Level $80$
Weight $2$
Character orbit 80.c
Rep. character $\chi_{80}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 18 4 14
Cusp forms 6 2 4
Eisenstein series 12 2 10

Trace form

\( 2 q - 2 q^{5} - 2 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{5} - 2 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{19} + 8 q^{21} - 6 q^{25} - 4 q^{29} + 8 q^{35} + 16 q^{39} + 4 q^{41} + 2 q^{45} + 6 q^{49} - 8 q^{55} - 24 q^{59} - 20 q^{61} + 16 q^{65} + 8 q^{69} - 16 q^{71} + 16 q^{75} + 32 q^{79} - 22 q^{81} - 12 q^{89} - 16 q^{91} + 8 q^{95} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.2.c.a 80.c 5.b $2$ $0.639$ \(\Q(\sqrt{-1}) \) None 40.2.c.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+(\beta-1)q^{5}-\beta q^{7}-q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)