Properties

Label 8029.2.a
Level 8029
Weight 2
Character orbit a
Rep. character \(\chi_{8029}(1,\cdot)\)
Character field \(\Q\)
Dimension 539
Newforms 8
Sturm bound 1621
Trace bound 2

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Defining parameters

Level: \( N \) = \( 8029 = 7 \cdot 31 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8029.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(1621\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8029))\).

Total New Old
Modular forms 812 539 273
Cusp forms 805 539 266
Eisenstein series 7 0 7

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

\(7\)\(31\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(66\)
\(+\)\(+\)\(-\)\(-\)\(71\)
\(+\)\(-\)\(+\)\(-\)\(69\)
\(+\)\(-\)\(-\)\(+\)\(64\)
\(-\)\(+\)\(+\)\(-\)\(69\)
\(-\)\(+\)\(-\)\(+\)\(64\)
\(-\)\(-\)\(+\)\(+\)\(66\)
\(-\)\(-\)\(-\)\(-\)\(70\)
Plus space\(+\)\(260\)
Minus space\(-\)\(279\)

Trace form

\(539q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 533q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 559q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(539q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 533q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 559q^{9} \) \(\mathstrut +\mathstrut 14q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 28q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 541q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 42q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 525q^{25} \) \(\mathstrut -\mathstrut 42q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 22q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut -\mathstrut 35q^{32} \) \(\mathstrut +\mathstrut 48q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 537q^{36} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 52q^{38} \) \(\mathstrut +\mathstrut 32q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 68q^{43} \) \(\mathstrut -\mathstrut 28q^{44} \) \(\mathstrut -\mathstrut 78q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 164q^{48} \) \(\mathstrut +\mathstrut 539q^{49} \) \(\mathstrut +\mathstrut 55q^{50} \) \(\mathstrut +\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 62q^{52} \) \(\mathstrut -\mathstrut 46q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 72q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 48q^{57} \) \(\mathstrut -\mathstrut 26q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 80q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 477q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 36q^{67} \) \(\mathstrut +\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 87q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 60q^{76} \) \(\mathstrut -\mathstrut 12q^{77} \) \(\mathstrut -\mathstrut 48q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 106q^{80} \) \(\mathstrut +\mathstrut 627q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 68q^{83} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 68q^{85} \) \(\mathstrut +\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 40q^{87} \) \(\mathstrut +\mathstrut 148q^{88} \) \(\mathstrut -\mathstrut 50q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 40q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 104q^{95} \) \(\mathstrut -\mathstrut 196q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8029))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 31 37
8029.2.a.a \(64\) \(64.112\) None \(-7\) \(-12\) \(-4\) \(-64\) \(+\) \(-\) \(-\)
8029.2.a.b \(64\) \(64.112\) None \(-5\) \(-18\) \(-26\) \(64\) \(-\) \(+\) \(-\)
8029.2.a.c \(66\) \(64.112\) None \(-7\) \(-2\) \(-4\) \(-66\) \(+\) \(+\) \(+\)
8029.2.a.d \(66\) \(64.112\) None \(-5\) \(-12\) \(-26\) \(66\) \(-\) \(-\) \(+\)
8029.2.a.e \(69\) \(64.112\) None \(6\) \(6\) \(0\) \(-69\) \(+\) \(-\) \(+\)
8029.2.a.f \(69\) \(64.112\) None \(8\) \(12\) \(30\) \(69\) \(-\) \(+\) \(+\)
8029.2.a.g \(70\) \(64.112\) None \(5\) \(22\) \(24\) \(70\) \(-\) \(-\) \(-\)
8029.2.a.h \(71\) \(64.112\) None \(6\) \(8\) \(0\) \(-71\) \(+\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8029))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8029)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(217))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(259))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1147))\)\(^{\oplus 2}\)