Properties

Label 3525.1.l
Level $3525$
Weight $1$
Character orbit 3525.l
Rep. character $\chi_{3525}(1268,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $60$
Newform subspaces $4$
Sturm bound $480$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3525.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 705 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3525, [\chi])\).

Total New Old
Modular forms 84 68 16
Cusp forms 60 60 0
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 60 0 0 0

Trace form

\( 60 q + O(q^{10}) \) \( 60 q - 60 q^{16} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3525, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3525.1.l.a $4$ $1.759$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-47}) \) \(\Q(\sqrt{705}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{3}+3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots\)
3525.1.l.b $8$ $1.759$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{6}+\cdots\)
3525.1.l.c $16$ $1.759$ \(\Q(\zeta_{40})\) $D_{10}$ \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{40}^{13}+\zeta_{40}^{17})q^{2}-\zeta_{40}^{11}q^{3}+\cdots\)
3525.1.l.d $32$ $1.759$ \(\Q(\zeta_{120})\) $D_{30}$ \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{120}^{41}-\zeta_{120}^{49})q^{2}+\zeta_{120}^{43}q^{3}+\cdots\)