Space of modular forms of level 1536, weight 2, and Character 1536.c

• Label: 1536.2.c
• Level: $1536$
• Weight: $2$
• Character orbit: 1536.c
• Rep. character: $\chi_{1536}(1535,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $13$
• Sturm bound: $512$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1536 = 2^{9} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1536.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(512\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(23\), \(59\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1536, [\chi])\).

	Total	New	Old
Modular forms	288	64	224
Cusp forms	224	64	160
Eisenstein series	64	0	64

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(1536, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1536.2.c.a	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.b	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.c	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1-2\beta )q^{9}+\cdots\)
1536.2.c.d	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
1536.2.c.e	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.f	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots\)
1536.2.c.g	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-2\beta _{2}q^{5}+(2+\beta _{3})q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
1536.2.c.h	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}-2\beta _{2}q^{5}+(2-\beta _{3})q^{9}+\cdots\)
1536.2.c.i	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.j	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots\)
1536.2.c.k	$1536$	$2$	1536.c	12.b	$2$	$8$	$8$	$12.265$	8.0.40960000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
1536.2.c.l	$1536$	$2$	1536.c	12.b	$2$	$8$	$8$	$12.265$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{5}+\zeta_{24}^{2}q^{7}+3q^{9}+\cdots\)
1536.2.c.m	$1536$	$2$	1536.c	12.b	$2$	$16$	$16$	$12.265$	16.0.\(\cdots\).7	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}+\beta _{2}q^{5}-\beta _{6}q^{7}+\beta _{13}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1536, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1536, [\chi]) \cong \)