Properties

Label 267.2.a
Level 267
Weight 2
Character orbit a
Rep. character \(\chi_{267}(1,\cdot)\)
Character field \(\Q\)
Dimension 15
Newforms 6
Sturm bound 60
Trace bound 3

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Defining parameters

Level: \( N \) = \( 267 = 3 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 267.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(267))\).

Total New Old
Modular forms 32 15 17
Cusp forms 29 15 14
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.

\(3\)\(89\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(9\)

Trace form

\(15q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 11q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 11q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 14q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 21q^{25} \) \(\mathstrut +\mathstrut 22q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 28q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 20q^{31} \) \(\mathstrut -\mathstrut 29q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 10q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 11q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 36q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 32q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 17q^{48} \) \(\mathstrut +\mathstrut 7q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut 16q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 38q^{58} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 18q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 11q^{64} \) \(\mathstrut +\mathstrut 48q^{65} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut +\mathstrut 22q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 32q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut -\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut +\mathstrut 42q^{78} \) \(\mathstrut -\mathstrut 14q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 38q^{82} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 28q^{84} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut -\mathstrut 64q^{86} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut +\mathstrut 48q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 20q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 19q^{96} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut 35q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(267))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 89
267.2.a.a \(1\) \(2.132\) \(\Q\) None \(0\) \(-1\) \(4\) \(-2\) \(+\) \(-\) \(q-q^{3}-2q^{4}+4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
267.2.a.b \(1\) \(2.132\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(-\) \(+\) \(q+q^{3}-2q^{4}+2q^{7}+q^{9}+6q^{11}+\cdots\)
267.2.a.c \(3\) \(2.132\) \(\Q(\zeta_{14})^+\) None \(-4\) \(3\) \(-7\) \(-4\) \(-\) \(-\) \(q+(-1-\beta _{1})q^{2}+q^{3}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
267.2.a.d \(3\) \(2.132\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(-3\) \(-6\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+2\beta _{1}+\cdots)q^{5}+\cdots\)
267.2.a.e \(3\) \(2.132\) 3.3.169.1 None \(2\) \(3\) \(5\) \(-4\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
267.2.a.f \(4\) \(2.132\) 4.4.23377.1 None \(1\) \(-4\) \(3\) \(6\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(267))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(267)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 2}\)