Properties

Label 4027.2.a
Level 4027
Weight 2
Character orbit a
Rep. character \(\chi_{4027}(1,\cdot)\)
Character field \(\Q\)
Dimension 335
Newforms 3
Sturm bound 671
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(671\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4027))\).

Total New Old
Modular forms 336 336 0
Cusp forms 335 335 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.

\(4027\)Dim.
\(+\)\(159\)
\(-\)\(176\)

Trace form

\(335q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 334q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 329q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(335q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 334q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 329q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 28q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 328q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut +\mathstrut 341q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 28q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut -\mathstrut 26q^{32} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 284q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 60q^{42} \) \(\mathstrut -\mathstrut 30q^{43} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 26q^{46} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 94q^{48} \) \(\mathstrut +\mathstrut 341q^{49} \) \(\mathstrut -\mathstrut 22q^{50} \) \(\mathstrut -\mathstrut 22q^{51} \) \(\mathstrut -\mathstrut 52q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 72q^{54} \) \(\mathstrut +\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 36q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 60q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 308q^{64} \) \(\mathstrut +\mathstrut 50q^{65} \) \(\mathstrut -\mathstrut 24q^{66} \) \(\mathstrut -\mathstrut 54q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 18q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut -\mathstrut 48q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 52q^{75} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut +\mathstrut 46q^{77} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 18q^{80} \) \(\mathstrut +\mathstrut 303q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut +\mathstrut 32q^{83} \) \(\mathstrut -\mathstrut 46q^{84} \) \(\mathstrut +\mathstrut 60q^{85} \) \(\mathstrut -\mathstrut 36q^{86} \) \(\mathstrut -\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 72q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut +\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 40q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 26q^{94} \) \(\mathstrut -\mathstrut 32q^{95} \) \(\mathstrut -\mathstrut 64q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut 14q^{98} \) \(\mathstrut -\mathstrut 14q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4027))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 4027
4027.2.a.a \(2\) \(32.156\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-2\) \(-7\) \(-\) \(q-\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
4027.2.a.b \(159\) \(32.156\) None \(-22\) \(-19\) \(-70\) \(-19\) \(+\)
4027.2.a.c \(174\) \(32.156\) None \(21\) \(17\) \(72\) \(24\) \(-\)