Properties

Label 1575.1.cp
Level 1575
Weight 1
Character orbit cp
Rep. character \(\chi_{1575}(193,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 8
Newform subspaces 1
Sturm bound 240
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1575.cp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1575, [\chi])\).

Total New Old
Modular forms 56 24 32
Cusp forms 8 8 0
Eisenstein series 48 16 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 8 0 0

Trace form

\( 8q + 4q^{6} + O(q^{10}) \) \( 8q + 4q^{6} - 4q^{16} + 8q^{21} - 4q^{26} + 4q^{31} - 4q^{41} + 4q^{51} - 8q^{56} - 4q^{61} - 16q^{71} - 8q^{81} - 8q^{86} + 4q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1575.1.cp.a \(8\) \(0.786\) \(\Q(\zeta_{24})\) \(A_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{6}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$3$ \( ( 1 + T^{4} )^{2} \)
$5$ 1
$7$ \( ( 1 + T^{4} )^{2} \)
$11$ \( ( 1 + T^{2} )^{8} \)
$13$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$17$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$19$ \( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \)
$23$ \( ( 1 + T^{4} )^{4} \)
$29$ \( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \)
$31$ \( ( 1 - T )^{8}( 1 + T + T^{2} )^{4} \)
$37$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$41$ \( ( 1 + T )^{8}( 1 - T + T^{2} )^{4} \)
$43$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$47$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$53$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$59$ \( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \)
$61$ \( ( 1 + T )^{8}( 1 - T + T^{2} )^{4} \)
$67$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$71$ \( ( 1 + T )^{16} \)
$73$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$79$ \( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \)
$83$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
$89$ \( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \)
$97$ \( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \)
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