Properties

Label 1792.3.g
Level $1792$
Weight $3$
Character orbit 1792.g
Rep. character $\chi_{1792}(127,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $9$
Sturm bound $768$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1792.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(768\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1792, [\chi])\).

Total New Old
Modular forms 536 96 440
Cusp forms 488 96 392
Eisenstein series 48 0 48

Trace form

\( 96q + 288q^{9} + O(q^{10}) \) \( 96q + 288q^{9} - 480q^{25} - 672q^{49} - 64q^{65} - 192q^{73} + 864q^{81} + 320q^{89} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1792.3.g.a \(4\) \(48.828\) \(\Q(i, \sqrt{7})\) None \(0\) \(-8\) \(0\) \(0\) \(q-2q^{3}+(\beta _{1}-2\beta _{3})q^{5}+\beta _{3}q^{7}-5q^{9}+\cdots\)
1792.3.g.b \(4\) \(48.828\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+4\beta _{1}q^{5}-\beta _{3}q^{7}+19q^{9}+\cdots\)
1792.3.g.c \(4\) \(48.828\) \(\Q(i, \sqrt{7})\) None \(0\) \(8\) \(0\) \(0\) \(q+2q^{3}+(-\beta _{1}+2\beta _{3})q^{5}+\beta _{3}q^{7}+\cdots\)
1792.3.g.d \(8\) \(48.828\) 8.0.1997017344.2 None \(0\) \(-8\) \(0\) \(0\) \(q+(-1+\beta _{1})q^{3}+(\beta _{5}-\beta _{6})q^{5}+\beta _{5}q^{7}+\cdots\)
1792.3.g.e \(8\) \(48.828\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}+(1+\beta _{5}+\cdots)q^{9}+\cdots\)
1792.3.g.f \(8\) \(48.828\) 8.0.1997017344.2 None \(0\) \(8\) \(0\) \(0\) \(q+(1-\beta _{1})q^{3}+(\beta _{5}-\beta _{6})q^{5}-\beta _{5}q^{7}+\cdots\)
1792.3.g.g \(12\) \(48.828\) 12.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}+(2+\beta _{7}+\cdots)q^{9}+\cdots\)
1792.3.g.h \(24\) \(48.828\) None \(0\) \(-16\) \(0\) \(0\)
1792.3.g.i \(24\) \(48.828\) None \(0\) \(16\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)