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Properties

Label 201.4.d
Level $201$
Weight $4$
Character orbit 201.d
Rep. character $\chi_{201}(200,\cdot)$
Character field $\Q$
Dimension $66$
Newform subspaces $2$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(201, [\chi])\).

Total New Old
Modular forms 70 70 0
Cusp forms 66 66 0
Eisenstein series 4 4 0

Trace form

\( 66 q + 252 q^{4} - 46 q^{6} - 32 q^{9} + O(q^{10}) \) \( 66 q + 252 q^{4} - 46 q^{6} - 32 q^{9} - 36 q^{10} + 20 q^{15} + 684 q^{16} + 16 q^{19} - 324 q^{21} + 96 q^{22} - 904 q^{24} + 1830 q^{25} - 236 q^{33} - 1142 q^{36} + 784 q^{37} + 472 q^{39} - 648 q^{40} - 2478 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 3312 q^{64} - 2632 q^{67} + 1588 q^{73} - 2420 q^{76} + 288 q^{81} + 4020 q^{82} - 6678 q^{84} + 2436 q^{88} + 746 q^{90} + 480 q^{91} + 208 q^{93} - 7032 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.d.a 201.d 201.d $2$ $11.859$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-8q^{4}-6\zeta_{6}q^{7}-3^{3}q^{9}+\cdots\)
201.4.d.b 201.d 201.d $64$ $11.859$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$