Properties

Label 2008.1.c
Level 2008
Weight 1
Character orbit c
Rep. character \(\chi_{2008}(501,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 2
Sturm bound 252
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2008.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2008 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(252\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2008, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + 6q^{4} - 2q^{7} + 6q^{9} + O(q^{10}) \) \( 6q + 6q^{4} - 2q^{7} + 6q^{9} + 6q^{16} - 2q^{17} - 2q^{22} - 2q^{23} + 6q^{25} - 2q^{28} - 2q^{31} + 6q^{36} - 2q^{38} - 2q^{41} + 4q^{49} - 2q^{58} - 2q^{63} + 6q^{64} - 2q^{68} - 2q^{73} - 2q^{74} - 2q^{79} + 6q^{81} - 2q^{86} - 2q^{88} - 2q^{89} - 2q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2008.1.c.a \(3\) \(1.002\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-502}) \) None \(-3\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{9}-\beta _{2}q^{11}+\cdots\)
2008.1.c.b \(3\) \(1.002\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-502}) \) None \(3\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\beta _{2}q^{11}+\cdots\)

Hecke characteristic polynomials

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