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

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

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

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