Properties

Label 1575.1.y
Level $1575$
Weight $1$
Character orbit 1575.y
Rep. character $\chi_{1575}(76,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.y (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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 28 16 12
Cusp forms 4 4 0
Eisenstein series 24 12 12

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

\( 4q + 2q^{4} - 4q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{9} + 2q^{11} - 2q^{16} - 2q^{21} + 4q^{29} - 2q^{36} - 2q^{39} + 4q^{44} + 2q^{49} - 4q^{51} - 4q^{64} - 4q^{71} - 2q^{79} + 4q^{81} - 4q^{84} - 4q^{91} - 2q^{99} + O(q^{100}) \)

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.y.a \(4\) \(0.786\) \(\Q(\zeta_{12})\) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-q^{9}+\cdots\)

Hecke characteristic polynomials

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