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

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

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 \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{4}+\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)