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Properties

Label 3700.1.ch
Level $3700$
Weight $1$
Character orbit 3700.ch
Rep. character $\chi_{3700}(487,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $8$
Newform subspaces $1$
Sturm bound $570$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3700.ch (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3700 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(570\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3700, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 8 8 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{8} - 2 q^{10} - 2 q^{16} - 8 q^{20} - 2 q^{25} - 2 q^{29} - 8 q^{32} - 8 q^{37} - 2 q^{40} + 2 q^{50} + 8 q^{53} + 2 q^{58} + 2 q^{61} - 2 q^{64} - 2 q^{73} - 2 q^{74}+ \cdots - 8 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(3700, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3700.1.ch.a 3700.ch 3700.bh $8$ $1.847$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-1}) \) None 3700.1.ch.a \(2\) \(0\) \(2\) \(0\) \(q+\zeta_{20}^{2}q^{2}+\zeta_{20}^{4}q^{4}+\zeta_{20}^{6}q^{5}+\cdots\)