Properties

Label 600.1.q
Level 600
Weight 1
Character orbit q
Rep. character \(\chi_{600}(107,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 12
Newform subspaces 2
Sturm bound 120
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 600.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(600, [\chi])\).

Total New Old
Modular forms 36 20 16
Cusp forms 12 12 0
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q + O(q^{10}) \) \( 12q - 12q^{16} - 12q^{51} + 12q^{66} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
600.1.q.a \(4\) \(0.299\) \(\Q(\zeta_{8})\) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots\)
600.1.q.b \(8\) \(0.299\) \(\Q(\zeta_{24})\) \(D_{6}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}^{4}q^{6}+\cdots\)

Hecke characteristic polynomials

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