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Properties

Label 20.5.f
Level $20$
Weight $5$
Character orbit 20.f
Rep. character $\chi_{20}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(20, [\chi])\).

Total New Old
Modular forms 30 4 26
Cusp forms 18 4 14
Eisenstein series 12 0 12

Trace form

\( 4 q - 10 q^{3} - 6 q^{5} + 110 q^{7} + O(q^{10}) \) \( 4 q - 10 q^{3} - 6 q^{5} + 110 q^{7} - 300 q^{11} - 360 q^{13} + 542 q^{15} + 960 q^{17} - 1996 q^{21} - 810 q^{23} + 1856 q^{25} + 2120 q^{27} - 836 q^{31} - 1660 q^{33} - 2562 q^{35} - 660 q^{37} + 2964 q^{41} + 3270 q^{43} + 1474 q^{45} - 2250 q^{47} + 1948 q^{51} + 1980 q^{53} - 6780 q^{55} - 13840 q^{57} + 15828 q^{61} + 12950 q^{63} - 732 q^{65} - 4810 q^{67} - 5988 q^{71} - 14060 q^{73} - 11282 q^{75} - 1020 q^{77} + 8176 q^{81} + 19950 q^{83} + 16376 q^{85} + 24800 q^{87} - 11124 q^{91} - 34060 q^{93} - 15576 q^{95} - 3180 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.5.f.a 20.f 5.c $4$ $2.067$ \(\Q(i, \sqrt{241})\) None \(0\) \(-10\) \(-6\) \(110\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2\beta _{1}+\beta _{3})q^{3}+(-6\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)