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Properties

Label 201.3.o
Level $201$
Weight $3$
Character orbit 201.o
Rep. character $\chi_{201}(17,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $860$
Newform subspaces $2$
Sturm bound $68$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.o (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 2 \)
Sturm bound: \(68\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(201, [\chi])\).

Total New Old
Modular forms 940 940 0
Cusp forms 860 860 0
Eisenstein series 80 80 0

Trace form

\( 860 q - 10 q^{3} - 122 q^{4} - 25 q^{6} - 32 q^{7} - 42 q^{9} + O(q^{10}) \) \( 860 q - 10 q^{3} - 122 q^{4} - 25 q^{6} - 32 q^{7} - 42 q^{9} - 50 q^{10} + 156 q^{12} - 15 q^{13} - 100 q^{15} + 102 q^{16} - 33 q^{18} + 20 q^{19} - 124 q^{21} + 256 q^{22} + 170 q^{24} + 334 q^{25} - 106 q^{27} - 644 q^{28} - 40 q^{30} + 59 q^{31} - 113 q^{33} + 10 q^{34} - 91 q^{36} + 28 q^{37} - 120 q^{39} - 172 q^{40} - 274 q^{42} + 172 q^{43} - 518 q^{45} + 1070 q^{46} + 233 q^{48} + 87 q^{49} - 37 q^{51} - 1196 q^{52} - 809 q^{54} - 1810 q^{55} + 105 q^{57} - 716 q^{58} - 2 q^{60} + 457 q^{61} + 102 q^{63} - 272 q^{64} - 814 q^{66} + 569 q^{67} - 123 q^{69} - 1296 q^{70} + 1196 q^{72} + 400 q^{73} + 358 q^{75} + 1380 q^{76} - 118 q^{78} + 318 q^{79} + 58 q^{81} + 2412 q^{82} - 431 q^{84} + 50 q^{85} - 954 q^{87} - 14 q^{88} - 504 q^{90} - 128 q^{91} - 1232 q^{93} - 1328 q^{94} + 1335 q^{96} + 77 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(201, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
201.3.o.a 201.o 201.o $20$ $5.477$ \(\Q(\zeta_{33})\) \(\Q(\sqrt{-3}) \) \(0\) \(6\) \(0\) \(2\) $\mathrm{U}(1)[D_{66}]$ \(q+(3\zeta_{33}^{2}+3\zeta_{33}^{13})q^{3}+4\zeta_{33}^{8}q^{4}+\cdots\)
201.3.o.b 201.o 201.o $840$ $5.477$ None \(0\) \(-16\) \(0\) \(-34\) $\mathrm{SU}(2)[C_{66}]$