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Properties

Label 8023.2.a
Level 8023
Weight 2
Character orbit a
Rep. character \(\chi_{8023}(1,\cdot)\)
Character field \(\Q\)
Dimension 653
Newforms 5
Sturm bound 1368
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1368\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8023))\).

Total New Old
Modular forms 686 653 33
Cusp forms 683 653 30
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.

\(71\)\(113\)FrickeDim.
\(+\)\(+\)\(+\)\(161\)
\(+\)\(-\)\(-\)\(172\)
\(-\)\(+\)\(-\)\(165\)
\(-\)\(-\)\(+\)\(155\)
Plus space\(+\)\(316\)
Minus space\(-\)\(337\)

Trace form

\( 653q + 3q^{2} + 655q^{4} - 2q^{5} - 16q^{7} + 15q^{8} + 653q^{9} + O(q^{10}) \) \( 653q + 3q^{2} + 655q^{4} - 2q^{5} - 16q^{7} + 15q^{8} + 653q^{9} + 6q^{10} - 4q^{11} + 16q^{12} - 10q^{13} + 8q^{14} + 16q^{15} + 671q^{16} + 10q^{17} + 25q^{18} - 16q^{19} - 20q^{20} - 24q^{21} + 8q^{22} + 4q^{23} + 10q^{24} + 647q^{25} - 6q^{26} + 12q^{27} - 44q^{28} - 18q^{29} - 14q^{30} - 12q^{31} - 17q^{32} - 12q^{33} + 54q^{34} + 20q^{35} + 659q^{36} + 6q^{37} - 46q^{38} - 4q^{39} + 6q^{40} - 2q^{41} - 20q^{42} - 16q^{43} - 44q^{44} - 22q^{45} + 12q^{46} - 36q^{47} - 14q^{48} + 557q^{49} - 83q^{50} + 52q^{51} - 10q^{52} + 34q^{53} - 72q^{54} - 4q^{55} - 12q^{56} + 8q^{57} - 50q^{58} + 20q^{59} - 10q^{60} - 6q^{61} - 48q^{62} - 16q^{63} + 703q^{64} + 16q^{65} + 92q^{66} + 16q^{67} - 130q^{68} + 52q^{69} - 48q^{70} - 13q^{71} + 31q^{72} - 34q^{73} - 20q^{74} - 24q^{75} - 24q^{76} - 4q^{77} - 48q^{78} - 40q^{79} - 58q^{80} + 645q^{81} + 42q^{82} - 36q^{83} - 20q^{84} + 48q^{85} - 24q^{86} - 32q^{87} - 24q^{88} - 38q^{89} - 88q^{90} - 40q^{91} - 20q^{92} + 16q^{93} - 4q^{94} - 8q^{95} + 12q^{96} - 42q^{97} - 29q^{98} + 24q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 71 113
8023.2.a.a \(3\) \(64.064\) \(\Q(\zeta_{14})^+\) None \(2\) \(3\) \(-1\) \(-2\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
8023.2.a.b \(155\) \(64.064\) None \(-21\) \(-16\) \(-26\) \(-40\) \(-\) \(-\)
8023.2.a.c \(158\) \(64.064\) None \(-24\) \(-23\) \(-31\) \(-2\) \(+\) \(+\)
8023.2.a.d \(165\) \(64.064\) None \(22\) \(18\) \(28\) \(24\) \(-\) \(+\)
8023.2.a.e \(172\) \(64.064\) None \(24\) \(18\) \(28\) \(4\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(113))\)\(^{\oplus 2}\)