Properties

Label 8014.2.a
Level $8014$
Weight $2$
Character orbit 8014.a
Rep. character $\chi_{8014}(1,\cdot)$
Character field $\Q$
Dimension $333$
Newform subspaces $5$
Sturm bound $2004$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 8014 = 2 \cdot 4007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8014.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(2004\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8014))\).

Total New Old
Modular forms 1004 333 671
Cusp forms 1001 333 668
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.

\(2\)\(4007\)FrickeDim
\(+\)\(+\)$+$\(76\)
\(+\)\(-\)$-$\(91\)
\(-\)\(+\)$-$\(90\)
\(-\)\(-\)$+$\(76\)
Plus space\(+\)\(152\)
Minus space\(-\)\(181\)

Trace form

\( 333 q - q^{2} + 333 q^{4} + 4 q^{5} - 4 q^{7} - q^{8} + 337 q^{9} + O(q^{10}) \) \( 333 q - q^{2} + 333 q^{4} + 4 q^{5} - 4 q^{7} - q^{8} + 337 q^{9} - 4 q^{10} + 6 q^{11} - 6 q^{13} + 333 q^{16} - 6 q^{17} - 5 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 10 q^{22} + 4 q^{23} + 327 q^{25} + 2 q^{26} - 4 q^{28} + 6 q^{29} - 16 q^{30} + 8 q^{31} - q^{32} + 28 q^{33} + 2 q^{34} + 4 q^{35} + 337 q^{36} - 6 q^{37} - 2 q^{38} + 12 q^{39} - 4 q^{40} - 2 q^{41} + 12 q^{42} + 4 q^{43} + 6 q^{44} + 8 q^{45} - 4 q^{47} + 345 q^{49} - 7 q^{50} - 16 q^{51} - 6 q^{52} + 16 q^{55} - 36 q^{57} - 10 q^{58} - 20 q^{59} - 10 q^{61} - 12 q^{62} - 24 q^{63} + 333 q^{64} - 52 q^{65} + 32 q^{66} - 30 q^{67} - 6 q^{68} + 16 q^{69} - 8 q^{70} - 5 q^{72} - 6 q^{73} + 2 q^{74} - 44 q^{75} - 2 q^{76} - 32 q^{77} - 12 q^{78} + 4 q^{79} + 4 q^{80} + 333 q^{81} - 6 q^{82} - 14 q^{83} + 4 q^{84} - 28 q^{85} - 4 q^{86} - 64 q^{87} - 10 q^{88} + 6 q^{89} - 36 q^{90} - 8 q^{91} + 4 q^{92} - 24 q^{93} + 8 q^{94} - 20 q^{95} - 34 q^{97} + 7 q^{98} + 38 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8014))\) 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 4007
8014.2.a.a 8014.a 1.a $2$ $63.992$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(1\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2\beta q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
8014.2.a.b 8014.a 1.a $76$ $63.992$ None \(-76\) \(2\) \(-18\) \(12\) $+$ $+$ $\mathrm{SU}(2)$
8014.2.a.c 8014.a 1.a $76$ $63.992$ None \(76\) \(-20\) \(-26\) \(-34\) $-$ $-$ $\mathrm{SU}(2)$
8014.2.a.d 8014.a 1.a $88$ $63.992$ None \(88\) \(22\) \(25\) \(33\) $-$ $+$ $\mathrm{SU}(2)$
8014.2.a.e 8014.a 1.a $91$ $63.992$ None \(-91\) \(-2\) \(22\) \(-14\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4007))\)\(^{\oplus 2}\)