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Properties

Label 3700.1.bu
Level $3700$
Weight $1$
Character orbit 3700.bu
Rep. character $\chi_{3700}(2043,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4$
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.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 740 \)
Character field: \(\Q(\zeta_{12})\)
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 60 20 40
Cusp forms 12 4 8
Eisenstein series 48 16 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 2 q^{4} + O(q^{10}) \) \( 4 q + 2 q^{4} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{29} + 6 q^{41} + 2 q^{53} - 4 q^{58} - 4 q^{61} - 4 q^{64} - 4 q^{68} - 2 q^{72} + 4 q^{73} - 4 q^{74} + 2 q^{81} - 2 q^{89} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bu.a 3700.bu 740.am $4$ $1.847$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-1}) \) None 740.1.bj.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3700, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3700, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(740, [\chi])\)\(^{\oplus 2}\)