Properties

Label 1792.1.c
Level $1792$
Weight $1$
Character orbit 1792.c
Rep. character $\chi_{1792}(769,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $256$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1792.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(256\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1792, [\chi])\).

Total New Old
Modular forms 30 10 20
Cusp forms 6 6 0
Eisenstein series 24 4 20

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

\( 6q - 2q^{9} + O(q^{10}) \) \( 6q - 2q^{9} - 2q^{25} + 6q^{49} + 8q^{57} - 8q^{65} - 2q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1792.1.c.a \(1\) \(0.894\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{9}+2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.b \(1\) \(0.894\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{9}-2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.c \(2\) \(0.894\) \(\Q(\sqrt{-2}) \) \(D_{4}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{3}-\beta q^{5}-q^{7}-q^{9}-\beta q^{13}+\cdots\)
1792.1.c.d \(2\) \(0.894\) \(\Q(\sqrt{-2}) \) \(D_{4}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-\beta q^{13}+\cdots\)