↑

Properties

Label 39.4.k
Level $39$
Weight $4$
Character orbit 39.k
Rep. character $\chi_{39}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $48$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(39, [\chi])\).

Total New Old
Modular forms 64 64 0
Cusp forms 48 48 0
Eisenstein series 16 16 0

Trace form

\( 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9} + O(q^{10}) \) \( 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9} - 156 q^{10} - 80 q^{13} + 70 q^{15} + 260 q^{16} + 256 q^{18} + 260 q^{19} + 82 q^{21} + 212 q^{22} - 1194 q^{24} - 248 q^{27} - 756 q^{28} - 1062 q^{30} - 180 q^{31} + 10 q^{33} - 396 q^{34} + 3060 q^{36} + 1932 q^{37} + 538 q^{39} + 360 q^{40} + 968 q^{42} + 1416 q^{43} - 386 q^{45} - 144 q^{46} - 410 q^{48} - 3000 q^{49} - 4336 q^{52} + 1930 q^{54} - 1012 q^{55} - 1274 q^{57} + 908 q^{58} - 2860 q^{60} + 836 q^{61} - 5150 q^{63} + 1376 q^{66} - 136 q^{67} - 1674 q^{69} + 1808 q^{70} - 3900 q^{72} + 3572 q^{73} + 5796 q^{75} + 8400 q^{76} + 12292 q^{78} - 3760 q^{79} + 2494 q^{81} + 2544 q^{82} + 1084 q^{84} + 4980 q^{85} + 2318 q^{87} - 8436 q^{88} - 8908 q^{91} - 1214 q^{93} - 8464 q^{94} - 6968 q^{96} - 204 q^{97} - 13094 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
39.4.k.a 39.k 39.k $48$ $2.301$ None \(0\) \(-2\) \(0\) \(20\) $\mathrm{SU}(2)[C_{12}]$