Properties

Label 3520.1.y
Level $3520$
Weight $1$
Character orbit 3520.y
Rep. character $\chi_{3520}(703,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $4$
Sturm bound $576$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3520.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 220 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(576\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3520, [\chi])\).

Total New Old
Modular forms 96 20 76
Cusp forms 48 12 36
Eisenstein series 48 8 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + O(q^{10}) \) \( 12 q + 12 q^{53} - 12 q^{81} - 12 q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3520.1.y.a 3520.y 220.i $2$ $1.757$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-i)q^{3}+iq^{5}+iq^{9}-iq^{11}+\cdots\)
3520.1.y.b 3520.y 220.i $2$ $1.757$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+i)q^{3}+iq^{5}+iq^{9}+iq^{11}+\cdots\)
3520.1.y.c 3520.y 220.i $4$ $1.757$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(\zeta_{12}^{4}-\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
3520.1.y.d 3520.y 220.i $4$ $1.757$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)