↑

Properties

Label 40.4.k
Level $40$
Weight $4$
Character orbit 40.k
Rep. character $\chi_{40}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 40.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(40, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 32 32 0
Eisenstein series 8 8 0

Trace form

\( 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8} + O(q^{10}) \) \( 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8} + 70 q^{10} - 8 q^{11} + 28 q^{12} + 72 q^{16} + 48 q^{17} - 278 q^{18} - 320 q^{20} + 68 q^{22} + 40 q^{25} - 92 q^{26} + 104 q^{27} + 620 q^{28} - 740 q^{30} + 288 q^{32} - 112 q^{33} - 460 q^{35} + 476 q^{36} + 636 q^{38} + 540 q^{40} - 8 q^{41} + 1020 q^{42} - 868 q^{43} + 1328 q^{46} - 784 q^{48} + 790 q^{50} + 1480 q^{51} - 1900 q^{52} - 2392 q^{56} + 104 q^{57} - 700 q^{58} - 1100 q^{60} - 2880 q^{62} + 520 q^{65} - 4360 q^{66} - 1852 q^{67} + 1196 q^{68} - 1500 q^{70} + 5596 q^{72} - 744 q^{73} + 3300 q^{75} + 4312 q^{76} + 2240 q^{78} + 1120 q^{80} - 1240 q^{81} + 5828 q^{82} + 2676 q^{83} + 6976 q^{86} - 2864 q^{88} + 4070 q^{90} - 1704 q^{91} - 7500 q^{92} - 10656 q^{96} - 584 q^{97} - 3814 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.4.k.a 40.k 40.k $32$ $2.360$ None \(-2\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$