Properties

Label 1400.1.bf
Level $1400$
Weight $1$
Character orbit 1400.bf
Rep. character $\chi_{1400}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1400, [\chi])\).

Total New Old
Modular forms 28 16 12
Cusp forms 4 4 0
Eisenstein series 24 12 12

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

\( 4q - 2q^{4} + 2q^{9} + O(q^{10}) \) \( 4q - 2q^{4} + 2q^{9} - 2q^{14} - 2q^{16} + 6q^{31} - 4q^{36} - 2q^{46} - 2q^{49} - 2q^{56} + 4q^{64} + 4q^{71} - 2q^{79} - 2q^{81} + 6q^{89} - 6q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1400.1.bf.a \(2\) \(0.699\) \(\Q(\sqrt{-3}) \) \(D_{6}\) None \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+q^{8}+\cdots\)
1400.1.bf.b \(2\) \(0.699\) \(\Q(\sqrt{-3}) \) \(D_{6}\) None \(\Q(\sqrt{2}) \) \(1\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}-q^{8}+\cdots\)