↑

Properties

Label 8006.2.a
Level $8006$
Weight $2$
Character orbit 8006.a
Rep. character $\chi_{8006}(1,\cdot)$
Character field $\Q$
Dimension $334$
Newform subspaces $4$
Sturm bound $2002$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8006.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(2002\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8006))\).

Total New Old
Modular forms 1003 334 669
Cusp forms 1000 334 666
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.

\(2\)\(4003\)FrickeDim
\(+\)\(+\)$+$\(75\)
\(+\)\(-\)$-$\(92\)
\(-\)\(+\)$-$\(98\)
\(-\)\(-\)$+$\(69\)
Plus space\(+\)\(144\)
Minus space\(-\)\(190\)

Trace form

\( 334 q + 334 q^{4} - 4 q^{5} + 2 q^{6} + 340 q^{9} + O(q^{10}) \) \( 334 q + 334 q^{4} - 4 q^{5} + 2 q^{6} + 340 q^{9} - 6 q^{10} + 2 q^{11} + 6 q^{13} + 334 q^{16} - 12 q^{17} + 10 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} + 328 q^{25} - 4 q^{26} - 6 q^{29} + 12 q^{30} - 20 q^{33} + 8 q^{34} - 24 q^{35} + 340 q^{36} - 6 q^{37} + 20 q^{39} - 6 q^{40} - 20 q^{41} + 16 q^{42} + 2 q^{44} - 32 q^{45} + 4 q^{46} + 8 q^{47} + 322 q^{49} + 8 q^{50} - 4 q^{51} + 6 q^{52} - 46 q^{53} + 8 q^{54} - 32 q^{55} + 40 q^{57} - 8 q^{58} - 10 q^{59} + 12 q^{61} - 4 q^{62} - 36 q^{63} + 334 q^{64} - 28 q^{65} + 16 q^{66} + 6 q^{67} - 12 q^{68} - 16 q^{69} - 8 q^{70} - 44 q^{71} - 20 q^{73} + 4 q^{74} + 4 q^{75} + 10 q^{76} - 4 q^{77} - 28 q^{78} - 12 q^{79} - 4 q^{80} + 342 q^{81} - 20 q^{82} - 6 q^{83} - 28 q^{85} - 2 q^{86} - 20 q^{87} + 4 q^{88} - 60 q^{89} - 14 q^{90} - 16 q^{91} - 8 q^{92} - 84 q^{93} - 16 q^{94} - 56 q^{95} + 2 q^{96} + 20 q^{97} - 32 q^{98} + 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8006))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 4003
8006.2.a.a 8006.a 1.a $69$ $63.928$ None \(69\) \(-15\) \(-9\) \(-29\) $-$ $-$ $\mathrm{SU}(2)$
8006.2.a.b 8006.a 1.a $75$ $63.928$ None \(-75\) \(1\) \(-9\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$
8006.2.a.c 8006.a 1.a $92$ $63.928$ None \(-92\) \(-2\) \(10\) \(8\) $+$ $-$ $\mathrm{SU}(2)$
8006.2.a.d 8006.a 1.a $98$ $63.928$ None \(98\) \(16\) \(4\) \(29\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4003))\)\(^{\oplus 2}\)