Properties

Label 201.2.d
Level 201
Weight 2
Character orbit d
Rep. character \(\chi_{201}(200,\cdot)\)
Character field \(\Q\)
Dimension 20
Newforms 1
Sturm bound 45
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 201.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(45\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

Trace form

\( 20q + 12q^{4} - 4q^{6} - 14q^{9} + O(q^{10}) \) \( 20q + 12q^{4} - 4q^{6} - 14q^{9} - 12q^{10} + 2q^{15} + 12q^{16} + 24q^{19} + 12q^{21} - 28q^{22} + 2q^{24} - 4q^{25} + 10q^{33} - 44q^{36} + 24q^{37} - 8q^{39} - 32q^{40} - 48q^{49} - 26q^{54} - 8q^{55} - 38q^{60} - 16q^{64} + 32q^{67} + 4q^{73} + 116q^{76} - 30q^{81} - 32q^{82} + 90q^{84} - 40q^{88} + 74q^{90} + 20q^{91} - 2q^{93} + 30q^{96} + O(q^{100}) \)

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.d.a \(20\) \(1.605\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(1+\beta _{16})q^{4}-\beta _{11}q^{5}+\cdots\)