↑

Properties

Label 20.4.e
Level $20$
Weight $4$
Character orbit 20.e
Rep. character $\chi_{20}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $14$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 20.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(20, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 14 14 0
Eisenstein series 8 8 0

Trace form

\( 14 q - 2 q^{2} - 4 q^{5} + 8 q^{6} - 44 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} - 4 q^{5} + 8 q^{6} - 44 q^{8} - 74 q^{10} - 80 q^{12} + 42 q^{13} + 184 q^{16} - 134 q^{17} + 306 q^{18} + 316 q^{20} - 144 q^{21} + 360 q^{22} + 106 q^{25} - 460 q^{26} - 880 q^{28} - 1240 q^{30} - 632 q^{32} + 80 q^{33} + 892 q^{36} + 326 q^{37} + 1600 q^{38} + 1836 q^{40} + 288 q^{41} + 1160 q^{42} + 586 q^{45} - 1432 q^{46} - 2720 q^{48} - 2214 q^{50} - 1524 q^{52} - 698 q^{53} + 2048 q^{56} - 960 q^{57} + 2712 q^{58} + 3280 q^{60} - 1832 q^{61} + 2440 q^{62} - 1778 q^{65} - 1680 q^{66} - 2428 q^{68} - 3040 q^{70} - 2172 q^{72} + 1942 q^{73} + 800 q^{76} + 3120 q^{77} + 3720 q^{78} + 2096 q^{80} + 4530 q^{81} + 536 q^{82} + 2282 q^{85} - 2552 q^{86} - 2400 q^{88} - 2154 q^{90} - 1840 q^{92} - 3280 q^{93} + 1088 q^{96} - 5994 q^{97} + 326 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.4.e.a 20.e 20.e $2$ $1.180$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots\)
20.4.e.b 20.e 20.e $12$ $1.180$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)