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Properties

Label 3660.1.eb
Level $3660$
Weight $1$
Character orbit 3660.eb
Rep. character $\chi_{3660}(419,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $64$
Newform subspaces $6$
Sturm bound $744$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 3660 = 2^{2} \cdot 3 \cdot 5 \cdot 61 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3660.eb (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3660 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 6 \)
Sturm bound: \(744\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3660, [\chi])\).

Total New Old
Modular forms 128 128 0
Cusp forms 64 64 0
Eisenstein series 64 64 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 64 0 0 0

Trace form

\( 64 q + 20 q^{6} - 8 q^{9} + O(q^{10}) \) \( 64 q + 20 q^{6} - 8 q^{9} + 16 q^{10} - 8 q^{21} - 8 q^{24} + 16 q^{30} - 12 q^{34} + 20 q^{36} + 4 q^{40} - 8 q^{54} + 8 q^{69} - 24 q^{70} - 20 q^{81} - 12 q^{84} - 8 q^{85} - 4 q^{90} - 8 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3660, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3660.1.eb.a 3660.eb 3660.db $8$ $1.827$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-15}) \) None 3660.1.eb.a \(-2\) \(-2\) \(0\) \(0\) \(q-\zeta_{20}^{2}q^{2}+\zeta_{20}^{8}q^{3}+\zeta_{20}^{4}q^{4}+\cdots\)
3660.1.eb.b 3660.eb 3660.db $8$ $1.827$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-15}) \) None 3660.1.eb.a \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{2}+\zeta_{20}^{8}q^{3}-\zeta_{20}^{8}q^{4}+\cdots\)
3660.1.eb.c 3660.eb 3660.db $8$ $1.827$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-15}) \) None 3660.1.eb.a \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{3}-\zeta_{20}^{8}q^{4}+\cdots\)
3660.1.eb.d 3660.eb 3660.db $8$ $1.827$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-15}) \) None 3660.1.eb.a \(2\) \(2\) \(0\) \(0\) \(q+\zeta_{20}^{2}q^{2}-\zeta_{20}^{8}q^{3}+\zeta_{20}^{4}q^{4}+\cdots\)
3660.1.eb.e 3660.eb 3660.db $16$ $1.827$ \(\Q(\zeta_{40})\) $D_{20}$ \(\Q(\sqrt{-5}) \) None 3660.1.eb.e \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{15}q^{3}-\zeta_{40}^{2}q^{4}+\cdots\)
3660.1.eb.f 3660.eb 3660.db $16$ $1.827$ \(\Q(\zeta_{40})\) $D_{20}$ \(\Q(\sqrt{-5}) \) None 3660.1.eb.e \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{17}q^{3}-\zeta_{40}^{2}q^{4}+\cdots\)