Properties

Label 8026.2.a
Level $8026$
Weight $2$
Character orbit 8026.a
Rep. character $\chi_{8026}(1,\cdot)$
Character field $\Q$
Dimension $334$
Newform subspaces $4$
Sturm bound $2007$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(2007\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8026))\).

Total New Old
Modular forms 1005 334 671
Cusp forms 1002 334 668
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.

\(2\)\(4013\)FrickeDim
\(+\)\(+\)$+$\(81\)
\(+\)\(-\)$-$\(86\)
\(-\)\(+\)$-$\(96\)
\(-\)\(-\)$+$\(71\)
Plus space\(+\)\(152\)
Minus space\(-\)\(182\)

Trace form

\( 334 q + 334 q^{4} + 4 q^{5} - 2 q^{6} + 328 q^{9} + O(q^{10}) \) \( 334 q + 334 q^{4} + 4 q^{5} - 2 q^{6} + 328 q^{9} + 6 q^{10} + 2 q^{11} - 2 q^{13} + 334 q^{16} + 16 q^{17} - 10 q^{19} + 4 q^{20} - 4 q^{22} + 12 q^{23} - 2 q^{24} + 340 q^{25} + 4 q^{26} - 24 q^{30} - 4 q^{31} - 20 q^{33} - 8 q^{34} + 4 q^{35} + 328 q^{36} - 4 q^{37} - 16 q^{38} - 56 q^{39} + 6 q^{40} + 12 q^{41} - 6 q^{43} + 2 q^{44} + 20 q^{45} - 8 q^{46} + 16 q^{47} + 346 q^{49} + 8 q^{50} - 16 q^{51} - 2 q^{52} + 10 q^{53} - 20 q^{54} + 32 q^{55} - 20 q^{57} + 10 q^{58} - 6 q^{59} - 22 q^{61} + 8 q^{62} - 44 q^{63} + 334 q^{64} - 4 q^{65} - 16 q^{66} - 14 q^{67} + 16 q^{68} - 28 q^{69} + 20 q^{70} + 4 q^{73} + 10 q^{74} - 28 q^{75} - 10 q^{76} + 16 q^{77} + 20 q^{78} - 20 q^{79} + 4 q^{80} + 294 q^{81} + 16 q^{82} - 2 q^{83} - 4 q^{85} - 8 q^{86} - 4 q^{87} - 4 q^{88} + 4 q^{89} + 30 q^{90} + 4 q^{91} + 12 q^{92} + 8 q^{93} + 4 q^{94} - 28 q^{95} - 2 q^{96} - 4 q^{97} + 46 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8026))\) 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 4013
8026.2.a.a 8026.a 1.a $71$ $64.088$ None \(71\) \(-9\) \(-34\) \(-19\) $-$ $-$ $\mathrm{SU}(2)$
8026.2.a.b 8026.a 1.a $81$ $64.088$ None \(-81\) \(-10\) \(-26\) \(3\) $+$ $+$ $\mathrm{SU}(2)$
8026.2.a.c 8026.a 1.a $86$ $64.088$ None \(-86\) \(11\) \(25\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$
8026.2.a.d 8026.a 1.a $96$ $64.088$ None \(96\) \(8\) \(39\) \(19\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8026))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4013))\)\(^{\oplus 2}\)