Properties

Label 6008.2.a
Level 6008
Weight 2
Character orbit a
Rep. character \(\chi_{6008}(1,\cdot)\)
Character field \(\Q\)
Dimension 188
Newform subspaces 5
Sturm bound 1504
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1504\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6008))\).

Total New Old
Modular forms 756 188 568
Cusp forms 749 188 561
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(751\)FrickeDim.
\(+\)\(+\)\(+\)\(44\)
\(+\)\(-\)\(-\)\(50\)
\(-\)\(+\)\(-\)\(50\)
\(-\)\(-\)\(+\)\(44\)
Plus space\(+\)\(88\)
Minus space\(-\)\(100\)

Trace form

\( 188q + 2q^{3} + 188q^{9} + O(q^{10}) \) \( 188q + 2q^{3} + 188q^{9} + 6q^{11} + 4q^{13} - 4q^{17} + 4q^{19} - 4q^{21} - 12q^{23} + 200q^{25} + 20q^{27} - 6q^{29} - 8q^{33} + 4q^{35} + 4q^{37} + 12q^{39} - 8q^{41} + 8q^{43} - 16q^{45} + 8q^{47} + 204q^{49} + 24q^{51} + 4q^{53} - 28q^{55} + 8q^{57} - 12q^{59} - 4q^{61} - 24q^{63} + 12q^{65} + 6q^{67} + 28q^{69} + 8q^{71} - 12q^{73} + 26q^{75} - 12q^{79} + 204q^{81} + 10q^{83} - 20q^{85} + 8q^{87} - 4q^{89} + 48q^{91} + 20q^{93} + 8q^{95} + 28q^{97} + 78q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6008))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 751
6008.2.a.a \(1\) \(47.974\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(-\) \(q-2q^{5}-4q^{7}-3q^{9}-q^{13}-6q^{17}+\cdots\)
6008.2.a.b \(44\) \(47.974\) None \(0\) \(-14\) \(7\) \(-20\) \(+\) \(+\)
6008.2.a.c \(44\) \(47.974\) None \(0\) \(-4\) \(-21\) \(-10\) \(-\) \(-\)
6008.2.a.d \(49\) \(47.974\) None \(0\) \(14\) \(-7\) \(22\) \(+\) \(-\)
6008.2.a.e \(50\) \(47.974\) None \(0\) \(6\) \(23\) \(12\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6008))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(751))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1502))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3004))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T^{2} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))
$11$ (\( 1 + 11 T^{2} \))
$13$ (\( 1 + T + 13 T^{2} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))
$19$ (\( 1 - 3 T + 19 T^{2} \))
$23$ (\( 1 + 9 T + 23 T^{2} \))
$29$ (\( 1 + 10 T + 29 T^{2} \))
$31$ (\( 1 + 8 T + 31 T^{2} \))
$37$ (\( 1 - 11 T + 37 T^{2} \))
$41$ (\( 1 + 41 T^{2} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))
$47$ (\( 1 + 3 T + 47 T^{2} \))
$53$ (\( 1 + T + 53 T^{2} \))
$59$ (\( 1 + 13 T + 59 T^{2} \))
$61$ (\( 1 - 3 T + 61 T^{2} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))
$71$ (\( 1 + 8 T + 71 T^{2} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))
$79$ (\( 1 - 6 T + 79 T^{2} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))
$89$ (\( 1 + 5 T + 89 T^{2} \))
$97$ (\( 1 + 3 T + 97 T^{2} \))
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