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

• 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: $57$

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

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

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.f.a	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(0\)	\(-4\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1792.2.f.b	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1792.2.f.c	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-2+\beta _{2})q^{7}-q^{9}+\cdots\)
1792.2.f.d	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(i, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{7}-3q^{9}-\beta _{1}q^{11}-2\beta _{3}q^{23}+\cdots\)
1792.2.f.e	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+3q^{9}+\cdots\)
1792.2.f.f	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
1792.2.f.g	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(2+\beta _{2})q^{7}-q^{9}+\cdots\)
1792.2.f.h	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{12}^{3})q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+\cdots\)
1792.2.f.i	$1792$	$2$	1792.f	28.d	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\zeta_{12}^{2})q^{5}+\cdots\)
1792.2.f.j	$1792$	$2$	1792.f	28.d	$2$	$8$	$8$	$14.309$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{6}q^{3}+\zeta_{24}^{2}q^{5}+(-\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
1792.2.f.k	$1792$	$2$	1792.f	28.d	$2$	$8$	$8$	$14.309$	8.0.629407744.1	\(\Q(\sqrt{-14}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{4}q^{3}+\beta _{1}q^{5}+\beta _{5}q^{7}+(3+\beta _{7})q^{9}+\cdots\)
1792.2.f.l	$1792$	$2$	1792.f	28.d	$2$	$8$	$8$	$14.309$	8.0.2517630976.5	\(\Q(\sqrt{-14}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \)