Space of modular forms of level 1024, weight 4, and Character 1024.b

• Label: 1024.4.b
• Level: $1024$
• Weight: $4$
• Character orbit: 1024.b
• Rep. character: $\chi_{1024}(513,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $13$
• Sturm bound: $512$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1024.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(512\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1024, [\chi])\).

	Total	New	Old
Modular forms	408	100	308
Cusp forms	360	92	268
Eisenstein series	48	8	40

Trace form

\( 92 q - 756 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1024, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1024.4.b.a	$1024$	$4$	1024.b	8.b	$2$	$2$	$2$	$60.418$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4\beta q^{3}+\beta q^{5}-8q^{7}-5q^{9}-4\beta q^{11}+\cdots\)
1024.4.b.b	$1024$	$4$	1024.b	8.b	$2$	$2$	$2$	$60.418$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-13\beta q^{5}+3^{3}q^{9}+55\beta q^{13}-104q^{17}+\cdots\)
1024.4.b.c	$1024$	$4$	1024.b	8.b	$2$	$2$	$2$	$60.418$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9\beta q^{5}+3^{3}q^{9}+37\beta q^{13}+104q^{17}+\cdots\)
1024.4.b.d	$1024$	$4$	1024.b	8.b	$2$	$2$	$2$	$60.418$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4\beta q^{3}-\beta q^{5}+8q^{7}-5q^{9}-4\beta q^{11}+\cdots\)
1024.4.b.e	$1024$	$4$	1024.b	8.b	$2$	$4$	$4$	$60.418$	\(\Q(\sqrt{-2}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-104\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3\beta _{1}+\beta _{2})q^{3}+(-3\beta _{1}-2\beta _{2})q^{5}+\cdots\)
1024.4.b.f	$1024$	$4$	1024.b	8.b	$2$	$4$	$4$	$60.418$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-11\beta _{1}q^{5}-3\beta _{3}q^{7}-13q^{9}+\cdots\)
1024.4.b.g	$1024$	$4$	1024.b	8.b	$2$	$4$	$4$	$60.418$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+7\beta _{1}q^{5}-\beta _{3}q^{7}-13q^{9}+\cdots\)
1024.4.b.h	$1024$	$4$	1024.b	8.b	$2$	$4$	$4$	$60.418$	\(\Q(\sqrt{-2}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(104\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3\beta _{1}+\beta _{2})q^{3}+(3\beta _{1}+2\beta _{2})q^{5}+(26+\cdots)q^{7}+\cdots\)
1024.4.b.i	$1024$	$4$	1024.b	8.b	$2$	$8$	$8$	$60.418$	8.0.\(\cdots\).12	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}+(-2\beta _{3}+\beta _{5})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
1024.4.b.j	$1024$	$4$	1024.b	8.b	$2$	$10$	$10$	$60.418$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}-\beta _{6}q^{5}+(-3-\beta _{2})q^{7}+(-6+\cdots)q^{9}+\cdots\)
1024.4.b.k	$1024$	$4$	1024.b	8.b	$2$	$10$	$10$	$60.418$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(28\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+\beta _{6}q^{5}+(3+\beta _{2})q^{7}+(-6+\cdots)q^{9}+\cdots\)
1024.4.b.l	$1024$	$4$	1024.b	8.b	$2$	$16$	$16$	$60.418$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{56}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}-\beta _{10}q^{5}-\beta _{7}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1024.4.b.m	$1024$	$4$	1024.b	8.b	$2$	$24$	$24$	$60.418$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1024, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1024, [\chi]) \cong \)