Properties

Label 16.5.f
Level $16$
Weight $5$
Character orbit 16.f
Rep. character $\chi_{16}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $14$
Newform subspaces $1$
Sturm bound $10$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(16, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 100 q^{10} + 94 q^{11} - 332 q^{12} - 2 q^{13} + 44 q^{14} - 168 q^{16} - 4 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20} - 164 q^{21} + 900 q^{22} + 1148 q^{23} - 1872 q^{24} - 3416 q^{26} - 1664 q^{27} - 3784 q^{28} + 862 q^{29} - 3740 q^{30} + 3208 q^{32} - 4 q^{33} + 7508 q^{34} + 1340 q^{35} + 11468 q^{36} - 1826 q^{37} + 3568 q^{38} + 2684 q^{39} - 5144 q^{40} - 17064 q^{42} + 1694 q^{43} - 14636 q^{44} + 1410 q^{45} - 5316 q^{46} + 6888 q^{48} + 682 q^{49} + 20070 q^{50} - 3012 q^{51} + 20452 q^{52} - 482 q^{53} + 10784 q^{54} - 11780 q^{55} - 6952 q^{56} - 20456 q^{58} - 2786 q^{59} - 29920 q^{60} - 3778 q^{61} - 11472 q^{62} + 15808 q^{64} - 2020 q^{65} + 30148 q^{66} + 7998 q^{67} + 18032 q^{68} + 9628 q^{69} + 15296 q^{70} + 19964 q^{71} - 17708 q^{72} - 23780 q^{74} + 17570 q^{75} - 23996 q^{76} - 9508 q^{77} - 8052 q^{78} + 1384 q^{80} + 1454 q^{81} + 16016 q^{82} - 17282 q^{83} + 19624 q^{84} + 9948 q^{85} - 4796 q^{86} - 49284 q^{87} + 7288 q^{88} - 5416 q^{90} - 28036 q^{91} - 14632 q^{92} + 8896 q^{93} + 432 q^{94} + 6064 q^{96} - 4 q^{97} - 12246 q^{98} + 49214 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.5.f.a 16.f 16.f $14$ $1.654$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots\)