Properties

Label 8021.2.a
Level 8021
Weight 2
Character orbit a
Rep. character \(\chi_{8021}(1,\cdot)\)
Character field \(\Q\)
Dimension 617
Newforms 4
Sturm bound 1442
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(1442\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8021))\).

Total New Old
Modular forms 722 617 105
Cusp forms 719 617 102
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.

\(13\)\(617\)FrickeDim.
\(+\)\(+\)\(+\)\(140\)
\(+\)\(-\)\(-\)\(169\)
\(-\)\(+\)\(-\)\(174\)
\(-\)\(-\)\(+\)\(134\)
Plus space\(+\)\(274\)
Minus space\(-\)\(343\)

Trace form

\( 617q + 3q^{2} + 4q^{3} + 623q^{4} + 2q^{5} + 15q^{8} + 621q^{9} + O(q^{10}) \) \( 617q + 3q^{2} + 4q^{3} + 623q^{4} + 2q^{5} + 15q^{8} + 621q^{9} + 10q^{10} + 12q^{11} + 28q^{12} - q^{13} + 12q^{14} + 16q^{15} + 647q^{16} + 14q^{17} + 39q^{18} + 20q^{19} + 30q^{20} - 8q^{21} + 8q^{22} + 20q^{23} + 24q^{24} + 603q^{25} - 3q^{26} + 28q^{27} - 2q^{29} - 36q^{30} + 16q^{31} + 23q^{32} + 8q^{33} - 2q^{34} + 16q^{35} + 623q^{36} - 2q^{37} - 8q^{38} + 4q^{39} + 6q^{40} + 30q^{41} + 12q^{43} + 56q^{44} + 42q^{45} + 24q^{46} + 20q^{47} + 72q^{48} + 589q^{49} - 7q^{50} + 28q^{51} + q^{52} + 10q^{53} + 16q^{54} + 8q^{55} + 8q^{56} + 20q^{57} - 38q^{58} + 8q^{59} - 12q^{60} - 10q^{61} - 16q^{62} + 36q^{63} + 683q^{64} + 2q^{65} - 56q^{66} + 52q^{67} + 30q^{68} + 20q^{69} - 84q^{70} + 20q^{71} + 95q^{72} + 2q^{73} - 38q^{74} + 96q^{75} + 92q^{76} + 24q^{77} - 8q^{78} - 8q^{79} - 14q^{80} + 625q^{81} + 10q^{82} + 16q^{83} - 16q^{84} + 16q^{85} + 28q^{86} + 68q^{87} + 52q^{88} - 38q^{89} + 6q^{90} - 8q^{91} + 4q^{92} - 72q^{93} + 16q^{94} + 12q^{95} - 32q^{96} - 18q^{97} - 21q^{98} + 72q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8021))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 13 617
8021.2.a.a \(134\) \(64.048\) None \(-6\) \(-33\) \(-8\) \(-32\) \(-\) \(-\)
8021.2.a.b \(140\) \(64.048\) None \(-6\) \(-9\) \(-12\) \(-32\) \(+\) \(+\)
8021.2.a.c \(169\) \(64.048\) None \(9\) \(9\) \(12\) \(36\) \(+\) \(-\)
8021.2.a.d \(174\) \(64.048\) None \(6\) \(37\) \(10\) \(28\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8021))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8021)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(617))\)\(^{\oplus 2}\)