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Properties

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

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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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(201, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
201.2.d.a 201.d 201.d $20$ $1.605$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(1+\beta _{16})q^{4}-\beta _{11}q^{5}+\cdots\)