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

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

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

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