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Properties

Label 201.3.g
Level $201$
Weight $3$
Character orbit 201.g
Rep. character $\chi_{201}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $86$
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.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q(\zeta_{6})\)
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 94 94 0
Cusp forms 86 86 0
Eisenstein series 8 8 0

Trace form

\( 86 q - 12 q^{3} + 78 q^{4} + 3 q^{6} - 12 q^{7} + 20 q^{9} + O(q^{10}) \) \( 86 q - 12 q^{3} + 78 q^{4} + 3 q^{6} - 12 q^{7} + 20 q^{9} + 6 q^{10} - 46 q^{12} - 29 q^{13} + 78 q^{15} - 146 q^{16} + 11 q^{18} + 46 q^{19} - 30 q^{21} + 140 q^{22} + 72 q^{24} - 378 q^{25} + 84 q^{27} - 16 q^{28} + 29 q^{30} - 15 q^{31} - 30 q^{33} - 54 q^{34} + 69 q^{36} - 50 q^{37} - 34 q^{39} + 128 q^{40} + 252 q^{42} + 26 q^{43} + 276 q^{45} - 146 q^{46} + 185 q^{48} - 131 q^{49} + 15 q^{51} - 608 q^{52} + 72 q^{54} + 28 q^{55} - 127 q^{57} - 120 q^{58} - 64 q^{60} + 115 q^{61} - 124 q^{63} - 476 q^{64} - 462 q^{66} - 569 q^{67} + 101 q^{69} + 636 q^{70} + 212 q^{72} + 95 q^{73} + 478 q^{75} + 248 q^{76} + 96 q^{78} + 331 q^{79} - 564 q^{81} - 344 q^{82} + 409 q^{84} - 94 q^{85} - 91 q^{87} + 234 q^{88} + 482 q^{90} - 444 q^{91} + 242 q^{93} + 580 q^{94} + 40 q^{96} - 99 q^{97} + 379 q^{99} + O(q^{100}) \)

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.g.a 201.g 201.g $2$ $5.477$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-6\) \(0\) \(-2\) $\mathrm{U}(1)[D_{6}]$ \(q-3q^{3}+(-4+4\zeta_{6})q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
201.3.g.b 201.g 201.g $84$ $5.477$ None \(0\) \(-6\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$