Space of modular forms of level 1792, weight 2, and Character 1792.e

• 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: $11$

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

\( 60 q - 44 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1792.2.e.a	$1792$	$2$	1792.e	56.e	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{5}+(-2-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1792.2.e.b	$1792$	$2$	1792.e	56.e	$2$	$4$	$4$	$14.309$	\(\Q(i, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{7}+3q^{9}-\beta _{2}q^{11}-2\beta _{3}q^{23}+\cdots\)
1792.2.e.c	$1792$	$2$	1792.e	56.e	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+(2+\zeta_{12}^{2})q^{7}+\cdots\)
1792.2.e.d	$1792$	$2$	1792.e	56.e	$2$	$8$	$8$	$14.309$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{2}+\beta _{5})q^{7}+\cdots\)
1792.2.e.e	$1792$	$2$	1792.e	56.e	$2$	$8$	$8$	$14.309$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1792.2.e.f	$1792$	$2$	1792.e	56.e	$2$	$8$	$8$	$14.309$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}^{2}q^{3}+\zeta_{16}^{4}q^{5}+(-\zeta_{16}-\zeta_{16}^{4}+\cdots)q^{7}+\cdots\)
1792.2.e.g	$1792$	$2$	1792.e	56.e	$2$	$8$	$8$	$14.309$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}^{2}q^{3}-\zeta_{16}^{4}q^{5}+(\zeta_{16}-\zeta_{16}^{4}+\cdots)q^{7}+\cdots\)
1792.2.e.h	$1792$	$2$	1792.e	56.e	$2$	$8$	$8$	$14.309$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{5}+\beta _{6}+\beta _{7})q^{5}+(\beta _{4}+\beta _{7})q^{7}+\cdots\)
1792.2.e.i	$1792$	$2$	1792.e	56.e	$2$	$8$	$8$	$14.309$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)