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Properties

Label 3620.1.dy
Level $3620$
Weight $1$
Character orbit 3620.dy
Rep. character $\chi_{3620}(219,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $48$
Newform subspaces $2$
Sturm bound $546$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 3620 = 2^{2} \cdot 5 \cdot 181 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3620.dy (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3620 \)
Character field: \(\Q(\zeta_{90})\)
Newform subspaces: \( 2 \)
Sturm bound: \(546\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3620, [\chi])\).

Total New Old
Modular forms 144 144 0
Cusp forms 48 48 0
Eisenstein series 96 96 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 48 0 0 0

Trace form

\( 48 q + 6 q^{5} - 6 q^{6} + O(q^{10}) \) \( 48 q + 6 q^{5} - 6 q^{6} + 6 q^{14} - 36 q^{21} + 6 q^{25} - 6 q^{30} + 6 q^{41} - 24 q^{49} + 6 q^{61} + 6 q^{64} - 6 q^{69} + 6 q^{70} - 6 q^{84} + 6 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3620, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3620.1.dy.a 3620.dy 3620.cy $24$ $1.807$ \(\Q(\zeta_{45})\) $D_{45}$ \(\Q(\sqrt{-5}) \) None 3620.1.dy.a \(0\) \(0\) \(3\) \(0\) \(q+\zeta_{90}^{43}q^{2}+(\zeta_{90}^{11}+\zeta_{90}^{35})q^{3}+\cdots\)
3620.1.dy.b 3620.dy 3620.cy $24$ $1.807$ \(\Q(\zeta_{45})\) $D_{45}$ \(\Q(\sqrt{-5}) \) None 3620.1.dy.a \(0\) \(0\) \(3\) \(0\) \(q-\zeta_{90}^{43}q^{2}+(-\zeta_{90}^{11}-\zeta_{90}^{35}+\cdots)q^{3}+\cdots\)