Space of modular forms of level 3072, weight 1, and Character 3072.i

• Label: 3072.1.i
• Level: $3072$
• Weight: $1$
• Character orbit: 3072.i
• Rep. character: $\chi_{3072}(257,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $8$
• Sturm bound: $512$
• Trace bound: $33$

Defining parameters

Level:	\( N \)	\(=\)	\( 3072 = 2^{10} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3072.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(512\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3072, [\chi])\).

	Total	New	Old
Modular forms	144	40	104
Cusp forms	48	24	24
Eisenstein series	96	16	80

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3072.1.i.a	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None					1536.1.e.b	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{3}+q^{9}+(i-1)q^{11}-2 i q^{17}+\cdots\)
3072.1.i.b	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None					1536.1.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{3}-q^{9}+(i-1)q^{11}+2 i q^{17}+\cdots\)
3072.1.i.c	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None					1536.1.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+i q^{3}-q^{9}+(-i+1)q^{11}+2 i q^{17}+\cdots\)
3072.1.i.d	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None					1536.1.e.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}+q^{9}+(-i+1)q^{11}-2 i q^{17}+\cdots\)
3072.1.i.e	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-6}) \)	None					1536.1.e.a	$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{8}^{3}q^{3}+(-1-\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
3072.1.i.f	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{3}) \)					384.1.h.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}-\zeta_{8}^{2}q^{25}+\cdots\)
3072.1.i.g	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{6}) \)					192.1.h.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{19}-\zeta_{8}^{2}q^{25}+\cdots\)
3072.1.i.h	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-6}) \)	None					1536.1.e.a	$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q+\zeta_{8}^{3}q^{3}+(1+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3072, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 3}\)