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Properties

Label 20.5.b
Level $20$
Weight $5$
Character orbit 20.b
Rep. character $\chi_{20}(11,\cdot)$
Character field $\Q$
Dimension $8$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
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 14 8 6
Cusp forms 10 8 2
Eisenstein series 4 0 4

Trace form

\( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} - 50 q^{10} - 200 q^{12} + 352 q^{13} - 168 q^{14} - 272 q^{16} - 48 q^{17} + 286 q^{18} - 300 q^{20} + 16 q^{21} + 800 q^{22} + 1552 q^{24} + 1000 q^{25} - 2172 q^{26} + 40 q^{28} + 1200 q^{29} + 1400 q^{30} - 2304 q^{32} - 1120 q^{33} - 2132 q^{34} - 1044 q^{36} - 5728 q^{37} - 3360 q^{38} - 2200 q^{40} + 4896 q^{41} + 12120 q^{42} + 7920 q^{44} - 400 q^{45} + 728 q^{46} + 8640 q^{48} - 5768 q^{49} + 750 q^{50} - 12488 q^{52} + 2592 q^{53} - 17776 q^{54} + 48 q^{56} + 3840 q^{57} - 7428 q^{58} - 9800 q^{60} + 7936 q^{61} + 25680 q^{62} + 18880 q^{64} - 1200 q^{65} - 8080 q^{66} + 2712 q^{68} - 2256 q^{69} + 12000 q^{70} - 36264 q^{72} - 14448 q^{73} - 18492 q^{74} + 12000 q^{76} + 2400 q^{77} - 14480 q^{78} - 13200 q^{80} - 936 q^{81} + 27412 q^{82} + 50464 q^{84} + 11200 q^{85} - 7392 q^{86} + 18080 q^{88} + 23760 q^{89} + 19350 q^{90} - 52680 q^{92} + 11360 q^{93} - 43368 q^{94} + 2688 q^{96} - 4368 q^{97} - 21474 q^{98} + O(q^{100}) \)

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.b.a 20.b 4.b $8$ $2.067$ 8.0.\(\cdots\).1 None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)