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Properties

Label 201.2.e
Level $201$
Weight $2$
Character orbit 201.e
Rep. character $\chi_{201}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $22$
Newform subspaces $3$
Sturm bound $45$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 50 22 28
Cusp forms 42 22 20
Eisenstein series 8 0 8

Trace form

\( 22 q - 4 q^{2} + 2 q^{3} - 14 q^{4} - 6 q^{7} + 12 q^{8} + 22 q^{9} + O(q^{10}) \) \( 22 q - 4 q^{2} + 2 q^{3} - 14 q^{4} - 6 q^{7} + 12 q^{8} + 22 q^{9} - 12 q^{10} + 6 q^{11} - 2 q^{12} - 3 q^{13} - 12 q^{14} - 4 q^{15} - 20 q^{16} + 4 q^{17} - 4 q^{18} - 6 q^{19} + 16 q^{20} - 4 q^{21} + 36 q^{22} - 2 q^{23} - 12 q^{24} + 14 q^{25} - 20 q^{26} + 2 q^{27} - 14 q^{28} + 2 q^{29} + 4 q^{30} - 29 q^{31} - 6 q^{32} + 2 q^{33} - 32 q^{34} + 30 q^{35} - 14 q^{36} + 8 q^{37} + 6 q^{38} - 9 q^{39} + 12 q^{40} + 6 q^{41} + 32 q^{42} - 14 q^{43} + 32 q^{44} + 16 q^{46} - 66 q^{47} - 20 q^{48} - 17 q^{49} - 26 q^{50} + 52 q^{52} - 40 q^{53} - 12 q^{56} - 12 q^{57} + 40 q^{58} + 12 q^{59} - 16 q^{60} + 15 q^{61} + 68 q^{62} - 6 q^{63} + 40 q^{64} + 24 q^{66} + 9 q^{67} - 92 q^{68} - 20 q^{70} + 28 q^{71} + 12 q^{72} + 19 q^{73} + 54 q^{74} + 14 q^{75} + 12 q^{76} + 36 q^{77} - 34 q^{78} + 5 q^{79} - 30 q^{80} + 22 q^{81} - 76 q^{82} + 14 q^{83} + 4 q^{84} + 6 q^{85} - 26 q^{86} - 22 q^{87} + 8 q^{88} - 8 q^{89} - 12 q^{90} - 80 q^{91} - 52 q^{92} - 5 q^{93} + 92 q^{94} - 10 q^{95} + 12 q^{96} - 7 q^{97} - 2 q^{98} + 6 q^{99} + O(q^{100}) \)

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.e.a 201.e 67.c $2$ $1.605$ \(\Q(\sqrt{-3}) \) None \(-2\) \(2\) \(-8\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+q^{3}-2\zeta_{6}q^{4}-4q^{5}+\cdots\)
201.2.e.b 201.e 67.c $10$ $1.605$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-10\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
201.2.e.c 201.e 67.c $10$ $1.605$ 10.0.\(\cdots\).1 None \(0\) \(10\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{9}q^{2}+q^{3}+(\beta _{1}-2\beta _{4}-2\beta _{5})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(201, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)