Properties

Label 8014.2.a
Level 8014
Weight 2
Character orbit 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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8014))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 4007
8014.2.a.a \(2\) \(63.992\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(1\) \(-1\) \(-\) \(+\) \(q+q^{2}-2\beta q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
8014.2.a.b \(76\) \(63.992\) None \(-76\) \(2\) \(-18\) \(12\) \(+\) \(+\)
8014.2.a.c \(76\) \(63.992\) None \(76\) \(-20\) \(-26\) \(-34\) \(-\) \(-\)
8014.2.a.d \(88\) \(63.992\) None \(88\) \(22\) \(25\) \(33\) \(-\) \(+\)
8014.2.a.e \(91\) \(63.992\) None \(-91\) \(-2\) \(22\) \(-14\) \(+\) \(-\)

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T )^{2} \))
$3$ (\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))
$5$ (\( 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} \))
$7$ (\( 1 + T + 3 T^{2} + 7 T^{3} + 49 T^{4} \))
$11$ (\( 1 + T + 11 T^{2} + 11 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 2 T + 22 T^{2} + 26 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 2 T - 10 T^{2} + 34 T^{3} + 289 T^{4} \))
$19$ (\( 1 - 3 T + 29 T^{2} - 57 T^{3} + 361 T^{4} \))
$23$ (\( 1 - T + 15 T^{2} - 23 T^{3} + 529 T^{4} \))
$29$ (\( ( 1 - 2 T + 29 T^{2} )^{2} \))
$31$ (\( 1 - 2 T + 58 T^{2} - 62 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 14 T + 118 T^{2} - 518 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 18 T + 158 T^{2} - 738 T^{3} + 1681 T^{4} \))
$43$ (\( 1 + 66 T^{2} + 1849 T^{4} \))
$47$ (\( 1 - 6 T + 98 T^{2} - 282 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 13 T + 117 T^{2} - 689 T^{3} + 2809 T^{4} \))
$59$ (\( 1 - 14 T + 122 T^{2} - 826 T^{3} + 3481 T^{4} \))
$61$ (\( ( 1 - 6 T + 61 T^{2} )^{2} \))
$67$ (\( 1 - T + 133 T^{2} - 67 T^{3} + 4489 T^{4} \))
$71$ (\( 1 - T - 9 T^{2} - 71 T^{3} + 5041 T^{4} \))
$73$ (\( 1 - 3 T + 137 T^{2} - 219 T^{3} + 5329 T^{4} \))
$79$ (\( ( 1 - 4 T + 79 T^{2} )^{2} \))
$83$ (\( 1 + 7 T + 167 T^{2} + 581 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 9 T + 197 T^{2} + 801 T^{3} + 7921 T^{4} \))
$97$ (\( 1 + 30 T + 414 T^{2} + 2910 T^{3} + 9409 T^{4} \))
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