Properties

Label 8005.2.a
Level 8005
Weight 2
Character orbit a
Rep. character \(\chi_{8005}(1,\cdot)\)
Character field \(\Q\)
Dimension 533
Newform subspaces 8
Sturm bound 1602
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 8005 = 5 \cdot 1601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8005.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(1602\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8005))\).

Total New Old
Modular forms 802 533 269
Cusp forms 799 533 266
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.

\(5\)\(1601\)FrickeDim.
\(+\)\(+\)\(+\)\(127\)
\(+\)\(-\)\(-\)\(139\)
\(-\)\(+\)\(-\)\(139\)
\(-\)\(-\)\(+\)\(128\)
Plus space\(+\)\(255\)
Minus space\(-\)\(278\)

Trace form

\( 533q - q^{2} + 527q^{4} + q^{5} - 4q^{6} - 8q^{7} - 9q^{8} + 537q^{9} + O(q^{10}) \) \( 533q - q^{2} + 527q^{4} + q^{5} - 4q^{6} - 8q^{7} - 9q^{8} + 537q^{9} - q^{10} + 4q^{12} - 10q^{13} + 4q^{14} - 4q^{15} + 503q^{16} + 2q^{17} - 9q^{18} - q^{20} - 16q^{21} - 24q^{22} - 16q^{23} + 533q^{25} - 2q^{26} - 24q^{27} - 36q^{28} - 14q^{29} + 8q^{30} - 28q^{31} - 9q^{32} - 26q^{34} - 4q^{35} + 539q^{36} - 14q^{37} + 24q^{38} - 24q^{39} - 9q^{40} + 26q^{41} + 56q^{42} - 4q^{43} + 16q^{44} + 13q^{45} - 12q^{46} + 28q^{47} + 28q^{48} + 533q^{49} - q^{50} + 8q^{51} - 82q^{52} - 18q^{53} + 68q^{54} - 4q^{55} + 32q^{56} + 4q^{57} - 54q^{58} + 16q^{59} - 34q^{61} + 4q^{62} + 12q^{63} + 431q^{64} + 2q^{65} + 56q^{66} - 12q^{67} + 26q^{68} - 4q^{69} + 12q^{70} - 16q^{71} - 29q^{72} - 26q^{73} - 50q^{74} - 12q^{76} - 40q^{77} + 76q^{78} - 24q^{79} - q^{80} + 557q^{81} - 14q^{82} + 20q^{83} - 32q^{84} - 18q^{85} + 20q^{86} - 8q^{87} - 104q^{88} + 34q^{89} + 7q^{90} - 48q^{91} - 96q^{92} - 76q^{93} - 64q^{94} + 4q^{95} + 116q^{96} - 2q^{97} + 43q^{98} + 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8005))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 1601
8005.2.a.a \(1\) \(63.920\) \(\Q\) None \(-1\) \(-2\) \(1\) \(2\) \(-\) \(-\) \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
8005.2.a.b \(1\) \(63.920\) \(\Q\) None \(-1\) \(2\) \(1\) \(2\) \(-\) \(-\) \(q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
8005.2.a.c \(2\) \(63.920\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(2\) \(-3\) \(-\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
8005.2.a.d \(2\) \(63.920\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}-q^{4}-q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)
8005.2.a.e \(126\) \(63.920\) None \(-15\) \(-46\) \(126\) \(-60\) \(-\) \(-\)
8005.2.a.f \(127\) \(63.920\) None \(-6\) \(-18\) \(-127\) \(28\) \(+\) \(+\)
8005.2.a.g \(137\) \(63.920\) None \(4\) \(20\) \(-137\) \(-30\) \(+\) \(-\)
8005.2.a.h \(137\) \(63.920\) None \(17\) \(46\) \(137\) \(53\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1601))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))(\( ( 1 - T + 2 T^{2} )^{2} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( ( 1 + T + 3 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 9 T^{4} \))
$5$ (\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))
$7$ (\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 3 T + 15 T^{2} + 21 T^{3} + 49 T^{4} \))(\( 1 + 12 T^{2} + 49 T^{4} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 8 T + 33 T^{2} + 88 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 44 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 8 T + 37 T^{2} + 104 T^{3} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))
$17$ (\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 15 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 26 T^{2} + 289 T^{4} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 3 T + 39 T^{2} + 57 T^{3} + 361 T^{4} \))(\( ( 1 + 19 T^{2} )^{2} \))
$23$ (\( 1 - 2 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 11 T + 65 T^{2} + 253 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 44 T^{2} + 184 T^{3} + 529 T^{4} \))
$29$ (\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 8 T + 69 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 - 8 T + 29 T^{2} )^{2} \))
$31$ (\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( 1 - 8 T + 70 T^{2} - 248 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 18 T + 150 T^{2} + 666 T^{3} + 1369 T^{4} \))(\( 1 + 2 T^{2} + 1369 T^{4} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 4 T + 81 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))
$43$ (\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 7 T + 97 T^{2} - 301 T^{3} + 1849 T^{4} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))
$47$ (\( 1 - 12 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 89 T^{2} + 2209 T^{4} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 13 T + 147 T^{2} + 689 T^{3} + 2809 T^{4} \))(\( 1 - 16 T + 162 T^{2} - 848 T^{3} + 2809 T^{4} \))
$59$ (\( 1 - 10 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 22 T + 234 T^{2} + 1298 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 40 T^{2} + 236 T^{3} + 3481 T^{4} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 77 T^{2} + 3721 T^{4} \))(\( 1 + 12 T + 126 T^{2} + 732 T^{3} + 3721 T^{4} \))
$67$ (\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( ( 1 + 9 T + 67 T^{2} )^{2} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))
$71$ (\( 1 - 10 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 25 T + 297 T^{2} + 1775 T^{3} + 5041 T^{4} \))(\( 1 + 12 T + 176 T^{2} + 852 T^{3} + 5041 T^{4} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 - 4 T + 105 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 154 T^{2} + 584 T^{3} + 5329 T^{4} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 6 T + 42 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 3 T + 167 T^{2} - 249 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 180 T^{2} + 1328 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 2 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + T + 77 T^{2} + 89 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 162 T^{2} + 712 T^{3} + 7921 T^{4} \))
$97$ (\( 1 - 10 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 14 T + 223 T^{2} + 1358 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 102 T^{2} + 1164 T^{3} + 9409 T^{4} \))
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