Properties

Label 201.3.c
Level $201$
Weight $3$
Character orbit 201.c
Rep. character $\chi_{201}(68,\cdot)$
Character field $\Q$
Dimension $44$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
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 44 4
Cusp forms 44 44 0
Eisenstein series 4 0 4

Trace form

\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + O(q^{10}) \) \( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99} + O(q^{100}) \)

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.c.a 201.c 3.b $44$ $5.477$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$