Properties

Label 2583.1.f
Level 2583
Weight 1
Character orbit f
Rep. character \(\chi_{2583}(2008,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 2
Sturm bound 336
Trace bound 7

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Defining parameters

Level: \( N \) \(=\) \( 2583 = 3^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2583.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(336\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2583, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 24 6 18
Eisenstein series 8 2 6

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

\( 6q + 2q^{2} + 4q^{4} + 4q^{8} + O(q^{10}) \) \( 6q + 2q^{2} + 4q^{4} + 4q^{8} + 2q^{16} + 2q^{23} + 6q^{25} + 6q^{32} - 2q^{37} - 2q^{43} - 4q^{46} + 6q^{49} + 2q^{50} - 10q^{74} + 4q^{86} - 2q^{91} - 8q^{92} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2583, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2583.1.f.a \(3\) \(1.289\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-287}) \) None \(1\) \(0\) \(0\) \(-3\) \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{4}-q^{7}+(\beta _{1}-\beta _{2})q^{8}+\cdots\)
2583.1.f.b \(3\) \(1.289\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-287}) \) None \(1\) \(0\) \(0\) \(3\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(1+\beta _{2})q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2583, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2583, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

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