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Properties

Label 201.2.a
Level $201$
Weight $2$
Character orbit 201.a
Rep. character $\chi_{201}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $5$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(45\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(201))\).

Total New Old
Modular forms 24 11 13
Cusp forms 21 11 10
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(67\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(8\)

Trace form

\( 11 q + q^{2} + q^{3} + 11 q^{4} - 6 q^{5} - 3 q^{6} + 9 q^{8} + 11 q^{9} + O(q^{10}) \) \( 11 q + q^{2} + q^{3} + 11 q^{4} - 6 q^{5} - 3 q^{6} + 9 q^{8} + 11 q^{9} - 6 q^{10} - q^{12} + 6 q^{13} - 2 q^{15} - q^{16} - 4 q^{17} + q^{18} - 6 q^{19} - 10 q^{20} + 4 q^{21} + 12 q^{22} - 10 q^{23} - 3 q^{24} - 11 q^{25} - 22 q^{26} + q^{27} + 8 q^{28} + 4 q^{29} + 2 q^{30} + 8 q^{31} + 9 q^{32} - 8 q^{33} - 10 q^{34} + 12 q^{35} + 11 q^{36} + 4 q^{37} - 24 q^{38} + 6 q^{39} - 30 q^{40} - 18 q^{41} - 8 q^{42} + 8 q^{43} - 20 q^{44} - 6 q^{45} - 16 q^{46} + 30 q^{47} - q^{48} + 11 q^{49} - q^{50} + 6 q^{51} - 22 q^{52} - 2 q^{53} - 3 q^{54} - 36 q^{56} + 12 q^{57} - 22 q^{58} + 6 q^{59} - 2 q^{60} + 18 q^{61} + 4 q^{62} + 23 q^{64} - 24 q^{65} - 12 q^{66} - 3 q^{67} - 10 q^{68} + 32 q^{70} + 8 q^{71} + 9 q^{72} - 28 q^{73} + 42 q^{74} + 7 q^{75} - 24 q^{76} + 12 q^{77} + 22 q^{78} + 40 q^{79} + 6 q^{80} + 11 q^{81} - 2 q^{82} + 4 q^{83} - 4 q^{84} - 36 q^{85} + 56 q^{86} + 10 q^{87} + 28 q^{88} - 28 q^{89} - 6 q^{90} + 8 q^{91} + 28 q^{92} - 4 q^{93} + 16 q^{94} + 64 q^{95} - 39 q^{96} - 14 q^{97} + 17 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(201))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 67
201.2.a.a 201.a 1.a $1$ $1.605$ \(\Q\) None \(-2\) \(-1\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}-6q^{11}+\cdots\)
201.2.a.b 201.a 1.a $1$ $1.605$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-5q^{7}+\cdots\)
201.2.a.c 201.a 1.a $1$ $1.605$ \(\Q\) None \(1\) \(-1\) \(-3\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
201.2.a.d 201.a 1.a $3$ $1.605$ 3.3.148.1 None \(3\) \(-3\) \(1\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
201.2.a.e 201.a 1.a $5$ $1.605$ 5.5.1025428.1 None \(0\) \(5\) \(-3\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(201))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(201)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 2}\)