Properties

Label 201.2.a
Level 201
Weight 2
Character orbit a
Rep. character \(\chi_{201}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 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: \(\Q\)
Newforms: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(201))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 67
201.2.a.a \(1\) \(1.605\) \(\Q\) None \(-2\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}-6q^{11}+\cdots\)
201.2.a.b \(1\) \(1.605\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-5\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-5q^{7}+\cdots\)
201.2.a.c \(1\) \(1.605\) \(\Q\) None \(1\) \(-1\) \(-3\) \(-3\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
201.2.a.d \(3\) \(1.605\) 3.3.148.1 None \(3\) \(-3\) \(1\) \(1\) \(+\) \(-\) \(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
201.2.a.e \(5\) \(1.605\) 5.5.1025428.1 None \(0\) \(5\) \(-3\) \(7\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)

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

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