Properties

Label 1400.1.c
Level $1400$
Weight $1$
Character orbit 1400.c
Rep. character $\chi_{1400}(349,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $240$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 26 10 16
Cusp forms 14 6 8
Eisenstein series 12 4 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + 6q^{9} + O(q^{10}) \) \( 6q + 6q^{9} + 6q^{44} - 6q^{46} - 6q^{49} + 6q^{56} - 6q^{64} - 6q^{74} + 6q^{81} - 6q^{86} + O(q^{100}) \)

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.c.a \(2\) \(0.699\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+q^{9}-q^{14}+\cdots\)
1400.1.c.b \(4\) \(0.699\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)