Properties

Label 1792.2.f
Level $1792$
Weight $2$
Character orbit 1792.f
Rep. character $\chi_{1792}(1791,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $12$
Sturm bound $512$
Trace bound $57$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(512\)
Trace bound: \(57\)
Distinguishing \(T_p\): \(3\), \(5\), \(29\), \(31\), \(37\)

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

\( 60q + 60q^{9} + O(q^{10}) \) \( 60q + 60q^{9} - 36q^{25} - 36q^{49} + 48q^{57} - 48q^{65} + 44q^{81} + O(q^{100}) \)

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.f.a \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(-8\) \(q+(-1-\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1792.2.f.b \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(8\) \(q+(-1-\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1792.2.f.c \(4\) \(14.309\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-2+\beta _{2})q^{7}-q^{9}+\cdots\)
1792.2.f.d \(4\) \(14.309\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{7}-3q^{9}-\beta _{1}q^{11}-2\beta _{3}q^{23}+\cdots\)
1792.2.f.e \(4\) \(14.309\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+3q^{9}+\cdots\)
1792.2.f.f \(4\) \(14.309\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
1792.2.f.g \(4\) \(14.309\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(2+\beta _{2})q^{7}-q^{9}+\cdots\)
1792.2.f.h \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(-8\) \(q+(1+\zeta_{12}^{3})q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+\cdots\)
1792.2.f.i \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(8\) \(q+(1+\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\zeta_{12}^{2})q^{5}+\cdots\)
1792.2.f.j \(8\) \(14.309\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{6}q^{3}+\zeta_{24}^{2}q^{5}+(-\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
1792.2.f.k \(8\) \(14.309\) 8.0.629407744.1 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{1}q^{5}+\beta _{5}q^{7}+(3+\beta _{7})q^{9}+\cdots\)
1792.2.f.l \(8\) \(14.309\) 8.0.2517630976.5 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)