Properties

Label 201.2.p
Level 201
Weight 2
Character orbit p
Rep. character \(\chi_{201}(2,\cdot)\)
Character field \(\Q(\zeta_{66})\)
Dimension 420
Newforms 2
Sturm bound 45
Trace bound 1

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Defining parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 201.p (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q(\zeta_{66})\)
Newforms: \( 2 \)
Sturm bound: \(45\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(201, [\chi])\).

Total New Old
Modular forms 500 500 0
Cusp forms 420 420 0
Eisenstein series 80 80 0

Trace form

\( 420q - 22q^{3} - 22q^{4} - 20q^{6} - 44q^{7} - 24q^{9} + O(q^{10}) \) \( 420q - 22q^{3} - 22q^{4} - 20q^{6} - 44q^{7} - 24q^{9} - 38q^{10} - 4q^{12} - 41q^{13} + 4q^{15} - 4q^{16} - 28q^{18} - 68q^{19} - 100q^{21} - 8q^{22} - 62q^{24} - 74q^{25} - 22q^{27} + 104q^{28} - 90q^{30} - 37q^{31} - 19q^{33} - 32q^{34} - 18q^{36} - 24q^{37} + 30q^{39} - 4q^{40} - 22q^{42} - 22q^{43} - 132q^{45} - 162q^{46} - 66q^{48} - 43q^{49} - 10q^{51} - 198q^{52} + 101q^{54} + 126q^{55} + 2q^{57} - 80q^{60} + 161q^{61} - 28q^{63} + 188q^{64} + q^{67} - q^{69} + 264q^{70} + 88q^{72} + 54q^{73} - 11q^{75} + 92q^{76} + 20q^{78} - 112q^{79} - 60q^{81} - 16q^{82} - 49q^{84} + 34q^{85} - 100q^{87} + 150q^{88} + 88q^{90} + 108q^{91} + 42q^{93} - 88q^{94} + 196q^{96} + 33q^{97} - 54q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(201, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
201.2.p.a \(20\) \(1.605\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-6\) \(q+(2\zeta_{33}+\zeta_{33}^{12})q^{3}-2\zeta_{33}^{4}q^{4}+\cdots\)
201.2.p.b \(400\) \(1.605\) None \(0\) \(-22\) \(0\) \(-38\)