Properties

Label 1792.2.e
Level $1792$
Weight $2$
Character orbit 1792.e
Rep. character $\chi_{1792}(895,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $9$
Sturm bound $512$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(512\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1792, [\chi])\).

Total New Old
Modular forms 280 68 212
Cusp forms 232 60 172
Eisenstein series 48 8 40

Trace form

\( 60q - 44q^{9} + O(q^{10}) \) \( 60q - 44q^{9} + 52q^{25} + 28q^{49} + 96q^{57} + 32q^{65} - 4q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1792.2.e.a \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-8\) \(q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{5}+(-2-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1792.2.e.b \(4\) \(14.309\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{7}+3q^{9}-\beta _{2}q^{11}-2\beta _{3}q^{23}+\cdots\)
1792.2.e.c \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+(2+\zeta_{12}^{2})q^{7}+\cdots\)
1792.2.e.d \(8\) \(14.309\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{2}+\beta _{5})q^{7}+\cdots\)
1792.2.e.e \(8\) \(14.309\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1792.2.e.f \(8\) \(14.309\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{3}+\zeta_{16}^{4}q^{5}+(-\zeta_{16}-\zeta_{16}^{4}+\cdots)q^{7}+\cdots\)
1792.2.e.g \(8\) \(14.309\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{3}-\zeta_{16}^{4}q^{5}+(\zeta_{16}-\zeta_{16}^{4}+\cdots)q^{7}+\cdots\)
1792.2.e.h \(8\) \(14.309\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(\beta _{5}+\beta _{6}+\beta _{7})q^{5}+(\beta _{4}+\beta _{7})q^{7}+\cdots\)
1792.2.e.i \(8\) \(14.309\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)