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Properties

Label 20.8.c
Level $20$
Weight $8$
Character orbit 20.c
Rep. character $\chi_{20}(9,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 20.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 \(M_{8}(20, [\chi])\).

Total New Old
Modular forms 24 4 20
Cusp forms 18 4 14
Eisenstein series 6 0 6

Trace form

\( 4 q - 156 q^{5} - 2036 q^{9} + O(q^{10}) \) \( 4 q - 156 q^{5} - 2036 q^{9} - 2640 q^{11} + 5552 q^{15} - 36336 q^{19} + 63104 q^{21} + 162036 q^{25} - 481896 q^{29} + 161344 q^{31} + 691248 q^{35} - 2366496 q^{39} + 1129464 q^{41} + 2391244 q^{45} - 4312452 q^{49} + 1978688 q^{51} + 4726640 q^{55} - 7747152 q^{59} + 4305128 q^{61} + 3389568 q^{65} - 9357248 q^{69} - 1206048 q^{71} + 3265888 q^{75} + 5716992 q^{79} + 570116 q^{81} - 8256064 q^{85} + 13641576 q^{89} - 7864224 q^{91} - 12453936 q^{95} + 47580560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.8.c.a 20.c 5.b $4$ $6.248$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(0\) \(-156\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-39-\beta _{1}+\beta _{2})q^{5}+(-5\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)