Space of modular forms of level 3072, weight 2, and Character 3072.d

• Label: 3072.2.d
• Level: $3072$
• Weight: $2$
• Character orbit: 3072.d
• Rep. character: $\chi_{3072}(1537,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $10$
• Sturm bound: $1024$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3072 = 2^{10} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3072.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1024\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).

	Total	New	Old
Modular forms	560	64	496
Cusp forms	464	64	400
Eisenstein series	96	0	96

Trace form

\( 64 q - 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3072, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3072.2.d.a	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}-q^{9}-\zeta_{8}^{2}q^{13}+\cdots\)
3072.2.d.b	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-q^{9}+4\zeta_{8}q^{11}+\cdots\)
3072.2.d.c	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3072.2.d.d	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{5}+3\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3072.2.d.e	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3072.2.d.f	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	8.0.18939904.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
3072.2.d.g	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{2}-\beta _{7})q^{7}-q^{9}+\cdots\)
3072.2.d.h	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{3}+(-\zeta_{24}^{2}-\zeta_{24}^{7})q^{5}+\zeta_{24}^{3}q^{7}+\cdots\)
3072.2.d.i	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	8.0.18939904.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
3072.2.d.j	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(2-\zeta_{16}^{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3072, [\chi]) \cong \)