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

• Label: 1792.2.b
• Level: $1792$
• Weight: $2$
• Character orbit: 1792.b
• Rep. character: $\chi_{1792}(897,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $16$
• Sturm bound: $512$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(512\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(23\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	280	48	232
Cusp forms	232	48	184
Eisenstein series	48	0	48

Trace form

\( 48 q - 48 q^{9} - 48 q^{25} + 48 q^{49} - 32 q^{65} + 32 q^{73} + 48 q^{81} + 32 q^{89}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1792.2.b.a	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					56.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+2\beta q^{5}-q^{7}-q^{9}-8 q^{15}+\cdots\)
1792.2.b.b	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					224.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-q^{7}-q^{9}-2\beta q^{11}-2\beta q^{13}+\cdots\)
1792.2.b.c	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					14.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-q^{7}-q^{9}+2\beta q^{13}+6 q^{17}+\cdots\)
1792.2.b.d	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					56.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}-q^{7}+3 q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.b.e	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					896.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{7}+3 q^{9}-\beta q^{11}+2\beta q^{13}-2 q^{17}+\cdots\)
1792.2.b.f	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					224.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+q^{7}-q^{9}-2\beta q^{11}+2\beta q^{13}+\cdots\)
1792.2.b.g	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					14.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+q^{7}-q^{9}-2\beta q^{13}+6 q^{17}+\cdots\)
1792.2.b.h	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					56.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-2\beta q^{5}+q^{7}-q^{9}+8 q^{15}+\cdots\)
1792.2.b.i	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					56.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}+q^{7}+3 q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.b.j	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	\(\Q(\sqrt{-1}) \)	None					896.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{7}+3 q^{9}+\beta q^{11}+2\beta q^{13}-2 q^{17}+\cdots\)
1792.2.b.k	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	\(\Q(i, \sqrt{5})\)	None					224.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.l	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None					896.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{3}-\beta_1 q^{5}-q^{7}+(\beta_{3}-1)q^{9}+\cdots\)
1792.2.b.m	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	\(\Q(i, \sqrt{5})\)	None					224.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.n	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	\(\Q(\zeta_{12})\)	None					896.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{3}+\beta_1 q^{5}+q^{7}+(\beta_{3}-1)q^{9}+\cdots\)
1792.2.b.o	$1792$	$2$	1792.b	8.b	$2$	$6$	$6$	$14.309$	6.0.399424.1	None					896.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
1792.2.b.p	$1792$	$2$	1792.b	8.b	$2$	$6$	$6$	$14.309$	6.0.399424.1	None					896.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)

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

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