Properties

Label 1575.1.x
Level $1575$
Weight $1$
Character orbit 1575.x
Rep. character $\chi_{1575}(451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1575.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 52 10 42
Cusp forms 4 4 0
Eisenstein series 48 6 42

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + 2q^{4} + O(q^{10}) \) \( 4q + 2q^{4} - 2q^{16} + 6q^{19} - 2q^{49} - 6q^{61} - 4q^{64} + 2q^{79} + 6q^{91} + O(q^{100}) \)

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.x.a \(2\) \(0.786\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}q^{4}-\zeta_{6}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+\cdots\)
1575.1.x.b \(2\) \(0.786\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{4}+\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)

Hecke characteristic polynomials

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