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Properties

Label 1400.1.bs
Level $1400$
Weight $1$
Character orbit 1400.bs
Rep. character $\chi_{1400}(181,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
Newform subspaces $3$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.bs (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1400 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{4} - 4 q^{9} - 4 q^{14} + 16 q^{15} - 4 q^{16} - 8 q^{18} - 8 q^{23} - 4 q^{30} - 4 q^{36} + 12 q^{39} + 16 q^{49} - 4 q^{50} - 4 q^{56} - 8 q^{57} - 4 q^{60} + 12 q^{63} - 4 q^{64} - 4 q^{65} - 8 q^{72} - 8 q^{78} + 8 q^{81} + 12 q^{92} - 4 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1400.1.bs.a 1400.bs 1400.as $4$ $0.699$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-14}) \) None \(-1\) \(-3\) \(1\) \(4\) \(q+\zeta_{10}^{4}q^{2}+(-1+\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
1400.1.bs.b 1400.bs 1400.as $4$ $0.699$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-14}) \) None \(-1\) \(3\) \(-1\) \(4\) \(q+\zeta_{10}^{4}q^{2}+(1-\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
1400.1.bs.c 1400.bs 1400.as $8$ $0.699$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(-8\) \(q-\zeta_{20}^{8}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}-\zeta_{20}^{6}q^{4}+\cdots\)