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Properties

Label 20.3.f
Level $20$
Weight $3$
Character orbit 20.f
Rep. character $\chi_{20}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 20.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(20, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 6 2 4
Eisenstein series 12 0 12

Trace form

\( 2 q + 2 q^{3} - 6 q^{5} - 14 q^{7} + O(q^{10}) \) \( 2 q + 2 q^{3} - 6 q^{5} - 14 q^{7} + 20 q^{11} + 18 q^{13} + 2 q^{15} + 2 q^{17} - 28 q^{21} - 46 q^{23} - 14 q^{25} + 32 q^{27} - 28 q^{31} + 20 q^{33} + 98 q^{35} + 66 q^{37} - 28 q^{41} - 30 q^{43} - 56 q^{45} - 78 q^{47} + 4 q^{51} - 14 q^{53} - 60 q^{55} - 16 q^{57} + 84 q^{61} + 98 q^{63} + 18 q^{65} - 14 q^{67} + 196 q^{71} + 98 q^{73} - 62 q^{75} - 140 q^{77} - 62 q^{81} - 126 q^{83} - 14 q^{85} - 16 q^{87} - 252 q^{91} - 28 q^{93} + 64 q^{95} + 66 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.3.f.a 20.f 5.c $2$ $0.545$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-6\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

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