Properties

Label 201.4.p
Level $201$
Weight $4$
Character orbit 201.p
Rep. character $\chi_{201}(2,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1320$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.p (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q(\zeta_{66})\)
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 1400 1400 0
Cusp forms 1320 1320 0
Eisenstein series 80 80 0

Trace form

\( 1320 q - 22 q^{3} + 214 q^{4} + q^{6} + 22 q^{7} + 48 q^{9} + O(q^{10}) \) \( 1320 q - 22 q^{3} + 214 q^{4} + q^{6} + 22 q^{7} + 48 q^{9} - 26 q^{10} - 4 q^{12} + 136 q^{13} + 166 q^{15} + 694 q^{16} - 181 q^{18} + 32 q^{19} + 1004 q^{21} + 544 q^{22} - 230 q^{24} - 2552 q^{25} - 22 q^{27} + 100 q^{28} + 810 q^{30} + 532 q^{31} + 800 q^{33} + 718 q^{34} - 243 q^{36} + 216 q^{37} - 1938 q^{39} + 820 q^{40} - 22 q^{42} + 1672 q^{43} + 4488 q^{45} - 3182 q^{46} + 2547 q^{48} - 2360 q^{49} + 287 q^{51} + 2156 q^{52} - 3793 q^{54} + 11272 q^{55} + 1091 q^{57} + 308 q^{58} - 56 q^{60} - 4544 q^{61} + 512 q^{63} - 22064 q^{64} - 1734 q^{67} + 350 q^{69} - 5588 q^{70} + 10648 q^{72} - 7992 q^{73} - 8459 q^{75} + 4540 q^{76} + 4664 q^{78} + 1178 q^{79} - 2448 q^{81} + 21556 q^{82} - 1183 q^{84} + 1864 q^{85} - 7051 q^{87} - 13694 q^{88} + 1138 q^{90} - 6308 q^{91} + 9792 q^{93} - 7172 q^{94} - 5417 q^{96} - 1140 q^{97} - 3678 q^{99} + O(q^{100}) \)

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.p.a 201.p 201.p $1320$ $11.859$ None \(0\) \(-22\) \(0\) \(22\) $\mathrm{SU}(2)[C_{66}]$