Properties

Label 20.3.b
Level $20$
Weight $3$
Character orbit 20.b
Rep. character $\chi_{20}(11,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 20.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
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 8 4 4
Cusp forms 4 4 0
Eisenstein series 4 0 4

Trace form

\( 4 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{9} - 10 q^{10} + 40 q^{12} - 16 q^{13} + 40 q^{14} - 16 q^{16} - 24 q^{17} + 22 q^{18} + 20 q^{20} + 40 q^{21} - 80 q^{22} - 80 q^{24} + 20 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} - 40 q^{30} + 128 q^{32} + 80 q^{33} + 92 q^{34} - 36 q^{36} + 16 q^{37} + 80 q^{38} + 40 q^{40} - 112 q^{41} - 120 q^{42} - 80 q^{44} - 40 q^{45} + 40 q^{46} - 4 q^{49} - 10 q^{50} + 56 q^{52} - 176 q^{53} + 80 q^{54} + 80 q^{56} - 36 q^{58} + 40 q^{60} + 128 q^{61} - 80 q^{62} - 64 q^{64} + 40 q^{65} + 80 q^{66} - 136 q^{68} + 120 q^{69} - 72 q^{72} + 264 q^{73} - 108 q^{74} + 240 q^{77} - 80 q^{78} - 80 q^{80} - 276 q^{81} + 116 q^{82} + 160 q^{84} - 160 q^{85} - 80 q^{86} + 160 q^{88} - 88 q^{89} + 30 q^{90} - 120 q^{92} - 400 q^{93} - 120 q^{94} - 264 q^{97} + 102 q^{98} + O(q^{100}) \)

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.b.a 20.b 4.b $4$ $0.545$ \(\Q(\zeta_{10})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots\)