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Properties

Label 8021.2.a
Level $8021$
Weight $2$
Character orbit 8021.a
Rep. character $\chi_{8021}(1,\cdot)$
Character field $\Q$
Dimension $617$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8021))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 13 617
8021.2.a.a 8021.a 1.a $134$ $64.048$ None \(-6\) \(-33\) \(-8\) \(-32\) $-$ $-$ $\mathrm{SU}(2)$
8021.2.a.b 8021.a 1.a $140$ $64.048$ None \(-6\) \(-9\) \(-12\) \(-32\) $+$ $+$ $\mathrm{SU}(2)$
8021.2.a.c 8021.a 1.a $169$ $64.048$ None \(9\) \(9\) \(12\) \(36\) $+$ $-$ $\mathrm{SU}(2)$
8021.2.a.d 8021.a 1.a $174$ $64.048$ None \(6\) \(37\) \(10\) \(28\) $-$ $+$ $\mathrm{SU}(2)$

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

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