Properties

Label 89.2.a
Level 89
Weight 2
Character orbit a
Rep. character \(\chi_{89}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 3
Sturm bound 15
Trace bound 2

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Defining parameters

Level: \( N \) = \( 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 89.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(15\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(89))\).

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 0
Eisenstein series 1 1 0

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

\(89\)Dim.
\(+\)\(1\)
\(-\)\(6\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 89
89.2.a.a \(1\) \(0.711\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-4\) \(+\) \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
89.2.a.b \(1\) \(0.711\) \(\Q\) None \(1\) \(2\) \(-2\) \(2\) \(-\) \(q+q^{2}+2q^{3}-q^{4}-2q^{5}+2q^{6}+2q^{7}+\cdots\)
89.2.a.c \(5\) \(0.711\) 5.5.535120.1 None \(-1\) \(-3\) \(-1\) \(8\) \(-\) \(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(3-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)