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Properties

Label 201.3.b
Level $201$
Weight $3$
Character orbit 201.b
Rep. character $\chi_{201}(133,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $1$
Sturm bound $68$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(68\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 48 22 26
Cusp forms 44 22 22
Eisenstein series 4 0 4

Trace form

\( 22 q - 52 q^{4} - 66 q^{9} + O(q^{10}) \) \( 22 q - 52 q^{4} - 66 q^{9} - 36 q^{10} + 72 q^{14} + 12 q^{15} + 116 q^{16} - 14 q^{17} - 26 q^{19} + 48 q^{21} + 32 q^{22} - 82 q^{23} + 36 q^{24} - 62 q^{25} - 100 q^{26} + 102 q^{29} + 36 q^{33} - 180 q^{35} + 156 q^{36} + 106 q^{37} - 72 q^{39} + 76 q^{40} + 154 q^{47} + 146 q^{49} - 224 q^{55} - 452 q^{56} + 370 q^{59} - 24 q^{60} - 300 q^{62} + 148 q^{64} - 284 q^{65} - 134 q^{67} - 116 q^{68} + 160 q^{71} + 218 q^{73} + 480 q^{76} - 396 q^{77} + 198 q^{81} - 68 q^{82} + 128 q^{83} + 20 q^{86} - 856 q^{88} - 118 q^{89} + 108 q^{90} - 400 q^{91} + 804 q^{92} - 72 q^{93} - 144 q^{96} + O(q^{100}) \)

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.b.a 201.b 67.b $22$ $5.477$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(201, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)