Properties

Label 1575.1.h
Level $1575$
Weight $1$
Character orbit 1575.h
Rep. character $\chi_{1575}(1126,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $5$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
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 40 10 30
Cusp forms 16 7 9
Eisenstein series 24 3 21

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 7 0 0 0

Trace form

\( 7q + 7q^{4} + q^{7} + O(q^{10}) \) \( 7q + 7q^{4} + q^{7} + 2q^{11} + 2q^{14} + 3q^{16} - q^{28} + 2q^{29} + 2q^{37} + 2q^{43} - 10q^{46} + 7q^{49} - 2q^{56} - 3q^{64} - 2q^{67} + 2q^{71} - 2q^{74} - 4q^{79} - 2q^{86} + O(q^{100}) \)

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

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

\( S_{1}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

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