Space of modular forms of level 1024, weight 2, and Character 1024.b

• Label: 1024.2.b
• Level: $1024$
• Weight: $2$
• Character orbit: 1024.b
• Rep. character: $\chi_{1024}(513,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $8$
• Sturm bound: $256$
• Trace bound: $33$

Defining parameters

Level:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(256\)
Trace bound:			\(33\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1024, [\chi])\).

	Total	New	Old
Modular forms	152	36	116
Cusp forms	104	28	76
Eisenstein series	48	8	40

Trace form

\( 28 q - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1024, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1024.2.b.a	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{3}+\beta q^{5}-4q^{7}-5q^{9}-2\beta q^{11}+\cdots\)
1024.2.b.b	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{5}-2q^{7}+q^{9}+\beta q^{11}+\cdots\)
1024.2.b.c	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{5}+3q^{9}-5\beta q^{13}-8q^{17}+3q^{25}+\cdots\)
1024.2.b.d	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3\beta q^{5}+3q^{9}+\beta q^{13}+8q^{17}-13q^{25}+\cdots\)
1024.2.b.e	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+\beta q^{5}+2q^{7}+q^{9}+\beta q^{11}+\cdots\)
1024.2.b.f	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{3}-\beta q^{5}+4q^{7}-5q^{9}-2\beta q^{11}+\cdots\)
1024.2.b.g	$1024$	$2$	1024.b	8.b	$2$	$8$	$8$	$8.177$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}^{2}q^{3}+\zeta_{16}q^{5}-\zeta_{16}^{3}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1024.2.b.h	$1024$	$2$	1024.b	8.b	$2$	$8$	$8$	$8.177$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1024, [\chi]) \cong \)