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Properties

Label 20.6.c
Level $20$
Weight $6$
Character orbit 20.c
Rep. character $\chi_{20}(9,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(20, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 12 2 10
Eisenstein series 6 0 6

Trace form

\( 2 q - 10 q^{5} + 238 q^{9} + O(q^{10}) \) \( 2 q - 10 q^{5} + 238 q^{9} - 200 q^{11} - 1240 q^{15} + 4488 q^{19} - 2728 q^{21} - 6150 q^{25} + 15708 q^{29} - 4288 q^{31} - 13640 q^{35} + 16368 q^{39} - 14828 q^{41} - 1190 q^{45} + 3606 q^{49} + 21824 q^{51} + 1000 q^{55} - 51944 q^{59} - 6116 q^{61} + 81840 q^{65} - 76136 q^{69} + 75216 q^{71} + 12400 q^{75} - 159456 q^{79} - 31942 q^{81} + 109120 q^{85} + 1652 q^{89} + 180048 q^{91} - 22440 q^{95} - 23800 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.6.c.a 20.c 5.b $2$ $3.208$ \(\Q(\sqrt{-31}) \) None 20.6.c.a \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+(-5-5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(20, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)