Properties

Label 1575.1.e
Level 1575
Weight 1
Character orbit e
Rep. character \(\chi_{1575}(874,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 3
Sturm bound 240
Trace bound 4

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1575.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(4\)

Dimensions

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

Total New Old
Modular forms 38 10 28
Cusp forms 14 8 6
Eisenstein series 24 2 22

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

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

Trace form

\( 8q - 6q^{4} + O(q^{10}) \) \( 8q - 6q^{4} + 2q^{11} - 2q^{14} + 4q^{16} - 2q^{29} - 10q^{46} - 8q^{49} - 2q^{56} + 4q^{64} + 2q^{71} + 2q^{74} + 2q^{79} - 2q^{86} + O(q^{100}) \)

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.e.a \(2\) \(0.786\) \(\Q(\sqrt{-1}) \) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{7}-iq^{8}+q^{11}-q^{14}+\cdots\)
1575.1.e.b \(2\) \(0.786\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-iq^{7}+q^{16}-iq^{28}-iq^{37}+\cdots\)
1575.1.e.c \(4\) \(0.786\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

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