↑

Properties

Label 201.4.f
Level $201$
Weight $4$
Character orbit 201.f
Rep. character $\chi_{201}(38,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $132$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(201, [\chi])\).

Total New Old
Modular forms 140 140 0
Cusp forms 132 132 0
Eisenstein series 8 8 0

Trace form

\( 132 q - 258 q^{4} - 23 q^{6} - 66 q^{7} - 70 q^{9} + O(q^{10}) \) \( 132 q - 258 q^{4} - 23 q^{6} - 66 q^{7} - 70 q^{9} - 18 q^{10} + 114 q^{12} - 180 q^{13} - 188 q^{15} - 738 q^{16} + 159 q^{18} - 208 q^{19} + 96 q^{21} - 324 q^{22} + 736 q^{24} + 2508 q^{25} + 1704 q^{28} - 843 q^{30} + 612 q^{31} + 146 q^{33} - 762 q^{34} + 221 q^{36} - 238 q^{37} - 394 q^{39} - 864 q^{40} - 3462 q^{46} + 951 q^{48} + 2316 q^{49} - 309 q^{51} - 376 q^{54} - 96 q^{55} - 1113 q^{57} + 122 q^{60} + 1728 q^{61} - 534 q^{63} + 900 q^{64} - 1214 q^{67} - 372 q^{69} + 578 q^{73} - 184 q^{76} - 4686 q^{78} + 4476 q^{79} + 666 q^{81} + 1368 q^{82} + 1161 q^{84} - 1908 q^{85} - 462 q^{87} + 2562 q^{88} - 1160 q^{90} - 3636 q^{91} - 1828 q^{93} - 3900 q^{96} + 1074 q^{97} + 906 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(201, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
201.4.f.a 201.f 201.f $132$ $11.859$ None \(0\) \(0\) \(0\) \(-66\) $\mathrm{SU}(2)[C_{6}]$