Properties

Label 1400.1.m
Level $1400$
Weight $1$
Character orbit 1400.m
Rep. character $\chi_{1400}(1301,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $5$
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.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
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 24 15 9
Cusp forms 12 9 3
Eisenstein series 12 6 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 9 0 0 0

Trace form

\( 9q + q^{2} + 3q^{4} + q^{7} + q^{8} - q^{9} + O(q^{10}) \) \( 9q + q^{2} + 3q^{4} + q^{7} + q^{8} - q^{9} - 5q^{14} + 3q^{16} - q^{18} - 2q^{23} + q^{28} + q^{32} + 5q^{36} - 8q^{39} - 6q^{44} - 4q^{46} + 9q^{49} + q^{56} - q^{63} + 9q^{64} + 2q^{71} - q^{72} + 6q^{74} + 2q^{79} + q^{81} - 6q^{86} - 2q^{92} + q^{98} + O(q^{100}) \)

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

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

\( S_{1}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)