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

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

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

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