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Properties

Label 8013.2.a
Level $8013$
Weight $2$
Character orbit 8013.a
Rep. character $\chi_{8013}(1,\cdot)$
Character field $\Q$
Dimension $445$
Newform subspaces $4$
Sturm bound $1781$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8013.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1781\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8013))\).

Total New Old
Modular forms 892 445 447
Cusp forms 889 445 444
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.

\(3\)\(2671\)FrickeDim
\(+\)\(+\)$+$\(116\)
\(+\)\(-\)$-$\(106\)
\(-\)\(+\)$-$\(129\)
\(-\)\(-\)$+$\(94\)
Plus space\(+\)\(210\)
Minus space\(-\)\(235\)

Trace form

\( 445 q + q^{2} + q^{3} + 449 q^{4} - 2 q^{5} + 3 q^{6} + 8 q^{7} + 9 q^{8} + 445 q^{9} + O(q^{10}) \) \( 445 q + q^{2} + q^{3} + 449 q^{4} - 2 q^{5} + 3 q^{6} + 8 q^{7} + 9 q^{8} + 445 q^{9} + 2 q^{10} - q^{12} + 2 q^{13} + 16 q^{14} + 6 q^{15} + 461 q^{16} - 6 q^{17} + q^{18} + 8 q^{19} + 22 q^{20} + 4 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 439 q^{25} + 2 q^{26} + q^{27} + 24 q^{28} + 2 q^{29} + 2 q^{30} + 24 q^{31} + 29 q^{32} + 4 q^{33} + 14 q^{34} + 16 q^{35} + 449 q^{36} + 2 q^{37} - 12 q^{38} + 6 q^{39} - 6 q^{40} - 22 q^{41} - 20 q^{42} - 20 q^{43} + 16 q^{44} - 2 q^{45} + 24 q^{47} + 15 q^{48} + 453 q^{49} - 17 q^{50} - 2 q^{51} - 14 q^{52} + 6 q^{53} + 3 q^{54} + 40 q^{55} + 40 q^{56} + 18 q^{58} + 8 q^{59} + 22 q^{60} - 6 q^{61} + 4 q^{62} + 8 q^{63} + 505 q^{64} - 44 q^{65} + 12 q^{66} + 24 q^{67} - 58 q^{68} - 36 q^{70} + 32 q^{71} + 9 q^{72} - 18 q^{73} + 10 q^{74} - 17 q^{75} + 100 q^{76} + 60 q^{77} + 2 q^{78} + 24 q^{79} - 6 q^{80} + 445 q^{81} - 54 q^{82} + 20 q^{83} + 20 q^{84} - 8 q^{85} + 44 q^{86} + 6 q^{87} + 40 q^{88} - 30 q^{89} + 2 q^{90} - 4 q^{91} + 4 q^{92} - 12 q^{93} + 8 q^{95} + 19 q^{96} + 14 q^{97} + 41 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8013))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 2671
8013.2.a.a 8013.a 1.a $94$ $63.984$ None \(-13\) \(94\) \(-14\) \(-55\) $-$ $-$ $\mathrm{SU}(2)$
8013.2.a.b 8013.a 1.a $106$ $63.984$ None \(15\) \(-106\) \(16\) \(35\) $+$ $-$ $\mathrm{SU}(2)$
8013.2.a.c 8013.a 1.a $116$ $63.984$ None \(-16\) \(-116\) \(-20\) \(-33\) $+$ $+$ $\mathrm{SU}(2)$
8013.2.a.d 8013.a 1.a $129$ $63.984$ None \(15\) \(129\) \(16\) \(61\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2671))\)\(^{\oplus 2}\)